The economic consequences of putting a price on carbon

The economic consequences of putting a priceon carbon*

Link to most recent version

Diego R. Känzig†

London Business School

September, 2021

Abstract

How does carbon pricing affect the economy? Is it successful at reducing

emissions and how does it affect economic inequality? Exploiting institu-

tional features of the European carbon market and high-frequency data, I

estimate the aggregate and distributional effects of a carbon policy shock. I

find that a shock tightening the carbon pricing regime leads to a significant

increase in energy prices and a persistent fall in emissions. The drop in emis-

sions comes at the cost of a temporary fall in economic activity, which is not

borne equally across society: poorer households lower their consumption

significantly while richer households are barely affected. My results suggest

that targeted fiscal policy can reduce the economic costs of carbon pricing –

without compromising emission reductions.

JEL classification: E32, E62, H23, Q54, Q58

Keywords: Carbon pricing, cap and trade, emissions, macroeconomic effects,

inequality, high-frequency identification

*I am indebted to my advisor Paolo Surico, João Cocco, Elias Papaioannou, Lucrezia Reich-lin and Hélène Rey for their invaluable guidance and support. For helpful comments and sug-gestions, I thank Asger Andersen, Michele Andreolli, Juan Antolin-Diaz, Christiane Baumeis-ter, Jean-Pierre Benoît, Florin Bilbiie, James Cloyne, Martin Ellison, Luis Fonseca, Luca Fornaro,Jordi Galí, Garth Heutel, Yueran Ma, Joseba Martinez, Matthias Meier, Silvia Miranda-Agrippino,Tsvetelina Nenova, Luca Neri, Gert Peersman, Michele Piffer, Richard Portes, Sebastian Rast,Vania Stavrakeva, Nadia Zhuravleva, Nathan Zorzi as well as participants at the EEA-ESEM con-ference, the Young Economist Symposium, the IAAE conference, the Oxford NuCamp PhD Work-shop, the IAEE conference, the Ghent Workshop on Empirical Macro, the QCGBF conference, theQMUL Economics and Finance Workshop and the LBS Brownbag Seminar. I thank Mario Allozafor kindly sharing their fiscal policy shock series. I also thank the IAEE for the best student paperaward. Finally, I am very grateful to the London Business School’s Wheeler Institute for Businessand Development for generously supporting this research.

†Contact: Diego R. Känzig, London Business School, Regent’s Park, London NW1 4SA, UnitedKingdom. E-mail: [email protected]. Web: diegokaenzig.com.

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1. Introduction

Climate change is one of the greatest challenges of our time, posing significantthreats not only to our lives, livelihoods and the environment, but also to theglobal economy. Fighting climate change, however, has proved very difficult be-cause of its global nature and the pervasive externalities involved. As the threatsof a climate crisis are becoming more acute and visible, climate change is now akey priority for policymakers around the world. There is broad agreement thatputting a price on carbon emissions is the most effective way to mitigate climatechange and several countries have enacted national carbon pricing policies, eithervia carbon taxes or cap and trade systems. Yet, little is known about the economiceffects of such policies. While arguably beneficial in the longer term, there couldbe short-term economic costs and important distributional consequences.

This paper aims to contribute filling this gap. I propose a novel approach toestimate the dynamic causal effects of a carbon policy shock, exploiting institu-tional features of the European carbon market and high-frequency data. The Eu-ropean Union Emissions Trading System (EU ETS) is the largest and oldest carbonmarket in the world, accounting for around 40 percent of the EU’s greenhousegas (GHG) emissions. The market was established in phases and the regulationshave been updated continuously. Following an event study approach, I collected113 regulatory update events concerning the supply of emission allowances. Bymeasuring the change in the carbon futures price in a tight window around theregulatory news, I am able to isolate a series of carbon policy surprises. Reversecausality can be plausibly ruled out as economic conditions are known and pricedby the market prior to the regulatory news and unlikely to change within the tightwindow. Using the surprise series as an instrument, I estimate the aggregate anddistributional effects of a structural carbon policy shock.

I find that carbon pricing has significant effects on emissions and the econ-omy. A carbon policy shock tightening the carbon pricing regime causes a strong,immediate increase in energy prices and a persistent fall in overall GHG emis-sions. Thus, carbon pricing turns out to be successful in achieving its goal ofreducing emissions. However, this does not come without cost. Consumer pricesrise significantly and economic activity falls, which is reflected in lower outputand higher unemployment. Crucially, the fall in activity appears to be somewhatless persistent than the fall in emissions – improving the emissions intensity inthe longer term. The stock market falls for about one and a half years but thenrebounds and turns positive after. The euro depreciates in real terms and importsfall significantly. While the shock leads to somewhat heightened financial un-

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certainty and a short-term deterioration of financial conditions, the main trans-mission channel appears to work through higher carbon prices, which passingthrough energy prices leads to lower consumption and investment. At the sametime, carbon pricing creates an incentive for green innovation, causing a signifi-cant uptick in low-carbon patenting.

Carbon policy shocks have also contributed meaningfully to historical varia-tions in prices, emissions and macroeconomic aggregates. Importantly, however,they did not account for the fall in emissions associated with the global financialcrisis – supporting the validity of the identified shock.

My results illustrate that carbon pricing is successful at reducing emissionsand mitigating climate change. However, this comes at the cost of lower eco-nomic activity today. Importantly, these costs are not equally distributed acrosssociety. Using detailed household-level data, I document pervasive heterogene-ity in the expenditure response to carbon policy shocks. While the expenditureof higher-income households only falls marginally, low-income households re-duce their expenditure significantly and persistently. These households are morehardly affected in two ways. First, they spend a larger share of their dispos-able income on energy and thus the higher energy bill leaves significantly lessresources for other expenditures. Second, they also experience the largest fall inincome, as they tend to work in sectors that are more exposed to carbon pricing.Crucially, the estimated magnitudes are much larger than what can be accountedfor by the direct effect through energy prices alone – pointing to an importantrole of indirect, general equilibrium effects via income and employment.

These findings suggest that targeted fiscal policies could be an effective wayto reduce the economic costs of carbon pricing. To the extent that energy demandis inelastic, which turns out to be the case especially for poorer households, thisshould not compromise the reductions in emissions. I also show that carbon pric-ing leads to a significant fall in the support of climate-related policies amonglow-income households. Thus, such targeted compensations may also help toincrease the public support of such policies.

A comprehensive series of sensitivity checks indicate that the results are ro-bust along a number of other dimensions including the selection of event dates,the estimation technique, the model specification, and the sample period. Im-portantly, the results are also robust to accounting for confounding news over theevent window. Controlling for such background noise using an heteroskedasticity-based estimator produces very similar results, even though the responses are a bitless precisely estimated.

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Related literature and contribution. This paper is related to a growing litera-ture studying the effects of climate policy and carbon pricing in particular. Whilethere is mounting evidence on the effectiveness of such policies for emission re-ductions (Lin and Li, 2011; Martin, De Preux, and Wagner, 2014; Andersson, 2019;Pretis, 2019), less is known about the economic effects. A number of studies haveanalyzed the macroeconomic effects of the British Columbia carbon tax, findingno significant impacts on GDP (Metcalf, 2019; Bernard, Kichian, and Islam, 2018).Metcalf and Stock (2020a,b) study the macroeconomic impacts of carbon taxes inEuropean countries. They find no robust evidence of a negative effect of the taxon employment or GDP growth.1 In contrast, theoretical studies based on com-putable general equilibrium models tend to find contractionary output effects(see e.g. McKibbin, Morris, and Wilcoxen, 2014; McKibbin et al., 2017; Goulderand Hafstead, 2018). By way of summary, the existing evidence on the economiceffects of carbon pricing is still scarce and inconclusive. I contribute to this litera-ture by providing new estimates for the macroeconomic impact based on the EUETS, the largest carbon market in the world.

A large literature has studied the macroeconomic effects of discretionary taxchanges more generally. To address the endogeneity of tax changes, the litera-ture has used SVAR techniques (Blanchard and Perotti, 2002) and narrative meth-ods (Romer and Romer, 2010). The narrative approach in particular points tolarge macroeconomic effects of tax changes; a tax increase leads to a significantand persistent decline of output and its components (see also Mertens and Ravn,2013; Cloyne, 2013). However, it is unclear how much we can learn from theseestimates with respect to carbon pricing, which is enacted to correct a clear exter-nality and not because of past decisions or ideology. While the motivation behindcarbon pricing is arguably long-term and thus more likely unrelated to the cur-rent state of the economy – similar to the tax changes considered in Romer andRomer (2010) – it is still perceivable that regulatory decisions also take economicconditions into account.

To address this potential endogeneity in carbon pricing, I propose a novelidentification strategy exploiting high-frequency variation. From a methodologi-cal viewpoint, my approach is closely related to the literature on high-frequencyidentification, which has been developed in the monetary policy setting (Kuttner,2001; Gürkaynak, Sack, and Swanson, 2005; Gertler and Karadi, 2015; Nakamuraand Steinsson, 2018, among others) and more recently employed in the global oil

1Contrary to this paper, Metcalf and Stock (2020a,b) do not study the effects of the EU ETS butnational carbon taxes, which are present in many European countries and cover sectors that arenot included in the EU ETS.

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market context (Känzig, 2021). In this literature, policy surprises are identified us-ing high-frequency asset price movements around policy events, such as FOMCor OPEC announcements. The idea is to isolate the impact of policy news by mea-suring the change in asset prices in a tight window around the announcements.I contribute to this literature by extending the high-frequency identification ap-proach to climate policy, exploiting institutional features of the European carbonmarket.

This paper is not the first to study regulatory news in the European carbonmarket. A number of studies have used event study techniques to analyze theeffects of regulatory news on carbon, energy and stock prices (Mansanet-Batallerand Pardo, 2009; Fan et al., 2017; Bushnell, Chong, and Mansur, 2013, amongothers). To the best of my knowledge, however, this paper is the first to exploitthese regulatory updates to analyze the economic effects of carbon pricing. Theapproach is very general and could also be employed to evaluate the performanceof other cap and trade systems.

Equipped with this novel identification strategy, I provide new direct ev-idence not only on the aggregate but also on the distributional consequencesof carbon pricing. There is growing consensus that a sustainable transition toa low-carbon economy has to be fair and equitable (see e.g. European Comis-sion, 2021). Therefore, it is crucial to understand how carbon pricing affectseconomic inequality. I find that carbon pricing in the EU has been more regres-sive than commonly thought, burdening lower-income households substantiallymore than richer ones. This stands in contrast to existing studies, which tendto find a more modest regressive impact (Beznoska, Cludius, and Steiner, 2012;Ohlendorf et al., 2021). My findings illustrate the importance of accounting forindirect, general-equilibrium effects via income and employment; solely focus-ing on the direct effects via higher energy prices can massively understate theactual distributional impact. Finally, I show that the distributional consequencesdo not only matter for inequality but also for the transmission of the policy to themacroeconomy.

Roadmap. The paper proceeds as follows. In the next section, I provide somebackground information on the European carbon market and detail relevant reg-ulatory events in this market. In Section 3, I discuss the high-frequency identifica-tion strategy and perform some diagnostic checks on the carbon policy surpriseseries. Section 4 discusses the econometric approach and introduces the exter-nal and internal instrument models. Section 5 presents the results on the aggre-gate effects of carbon pricing. I start by analyzing the instrument strength before

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studying the effects on emissions and the macroeconomy, the historical impor-tance and potential propagation channels. Section 6 looks into the heterogeneouseffects of carbon pricing, using detailed household-level data on income and ex-penditure. I analyze the distributional impact, how heterogeneity matters for thetransmission and end with some policy implications. In Section 7, I perform anumber of robustness checks. Section 8 concludes.

2. The European carbon market

The European emissions trading system is the cornerstone of the EU’s policy tocombat climate change. It is the largest carbon market in the world and also hasone of the longest implementation histories. Established in 2005, it covers morethan 11,000 heavy energy-using installations and airlines, accounting for around40 percent of the EU’s greenhouse gas emissions.

The market operates under the cap and trade principle. Different from a car-bon tax, a cap is set on the total amount of certain greenhouse gases that can beemitted by installations covered by the system. The cap is reduced over time sothat total emissions fall. Within the cap, emission allowances are auctioned off orallocated for free among the companies in the system, and can subsequently betraded. Alternatively, companies can also use limited amounts of internationalcredits from emission-saving projects around the world. Regulated companiesmust monitor and report their emissions. Each year, the companies must surren-der enough allowances to cover all their emissions. This is enforced with heavyfines. If a company reduces its emissions, it can keep the spare allowances tocover its future needs or sell them to another company that is short of allowances.A binding limit on the total number of allowances available in the system guar-antees a positive price on carbon (see European Comission, 2020a, for more infor-mation).

There exist several organized markets where EU emission allowances (EUAs)can be traded. An EUA is defined as the right to emit one ton of carbon diox-ide equivalent gas and is traded in spot markets such as Bluenext (Paris), EEX(Leipzig) or Nord Pool (Oslo). Furthermore, there exist also liquid futures mar-kets on EUAs, such as the EEX and ICE (London). In 2018, the cumulative trad-ing volume in the relevant futures and spot markets was about 10 billion EUA(DEHSt, 2019).

A brief history of the EU ETS. The development of the EU ETS has been di-vided into different phases. The evolution of the carbon price over the phases of

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the system is depicted in Figure 1. The first phase lasted three years, from 2005 to2007. This period was a pilot phase to prepare for phase two, where the systemhad to run efficiently to help the EU meet its Kyoto targets. In this initial phase,almost all allowances were freely allocated at the national level. In absence of reli-able emissions data, phase one caps were set on the basis of estimates. In 2007, thecarbon price fell significantly as it became apparent that the total amount of al-lowances issued exceeded total emissions significantly, and eventually convergedto zero as phase one allowances could not be transferred to phase two.

Figure 1: The carbon price in the EU

Notes: The EUA price, as measured by the price of the first EUA futures contractover the different phases of the EU ETS.

The second phase ran from 2008 until 2012, coinciding with the first commit-ment period of the Kyoto Protocol where the countries in the EU ETS had con-crete emission targets to meet. Because verified annual emissions data from thepilot phase was now available, the cap on allowances was reduced in phase two,based on actual emissions. The proportion of free allocation fell slightly, severalcountries started to hold auctions, and businesses were allowed to buy a limitedamount of international credits. The commission also started to extend the sys-tem to cover more gases and sectors; in 2012 the aviation sector was included,even though this only applies for flights within the European Economic Area.Despite these changes, EU carbon prices remained at moderate levels. This wasmainly because the 2008 economic crisis led to emissions reductions that weregreater than expected, which in turn led to a large surplus of allowances andcredits weighing down prices.

The subsequent third phase began in 2013 and ran until the end of 2020.Learning from the lessons of the previous phases, the system was changed sig-nificantly in a number of key respects. In particular, the new system relies on asingle, EU-wide cap on emissions in place of the previous national caps, auction-

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ing became the default method for allocating allowances instead of the previousfree allocation and harmonized allocation rules apply to the allowances still allo-cated for free, and the system covers more sectors and gases, in particular nitrousoxide and perfluorocarbons in addition to carbon dioxide. In 2014, the Commis-sion postponed the auctioning of 900 million allowances to address the surplus ofemission allowances that has built up since the Great Recession (‘back-loading’).Later, the Commission introduced a market stability reserve, which started oper-ating in January 2019. This reserve has the aim to reduce the current surplus ofallowances and improve the system’s resilience to major shocks by adjusting thesupply of allowances to be auctioned. To this end, the back-loaded allowanceswere transferred to the reserve rather than auctioned in the last years of phasethree and unallocated allowances were transferred to the reserve as well.

The current, fourth phase spans the period from 2021 to 2030. The legislativeframework for this trading period was revised in early 2018. In order to achievethe EU’s 2030 emission reduction targets, the pace of annual reductions in to-tal allowances is increased to 2.2 percent from the previous 1.74 percent and themarket stability reserve is reinforced to improve the EU ETS’s resilience to futureshocks. More recently, the Commission has proposed to further revise and ex-pand the scope of the EU ETS, with the aim to achieve a climate-neutral EU by2050 (see European Comission, 2020a).

Regulatory events. Given its pioneering role, the establishment of the Europeancarbon market has followed a learning-by-doing process. As illustrated above,since the start in 2005, the system has been expanded considerably and its insti-tutions and rules have been continuously updated to address issues encounteredin the market, improve market efficiency, and reduce information asymmetry andmarket distortions.

Building on the event study literature, I collected a comprehensive list of reg-ulatory events in the EU ETS. These regulatory update events can take the formof a decision of the European Commission, a vote of the European Parliament ora judgement of an European court, for instance. Of primary interest in this paperare regulatory news regarding the supply of emission allowances. Thus, I focus onnews concerning the overall cap in the EU ETS, the free allocation of allowances,the auctioning of allowances as well as the use of international credits. Goingthrough the official journal of the European Union as well as the European Com-mission Climate Action news archive, I could identify 113 such events during theperiod between 2005 and 2018. The events as well as the sources are detailed inTable A.1 in the Appendix. In the first two phases, the key events concern de-

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cisions on the national allocation plans (NAP) of the individual member states,e.g. the commission approving or rejecting allocation plans or a court ruling incase of legal conflicts about the free allocation of allowances. With the move toauctioning as the default way of allocating allowances, decisions on the timingand quantities of emission allowances to be auctioned became the most impor-tant regulatory news in phase three. After the pilot phase of the system, therewere also a number of important events related to the use and entitlement of in-ternational credits. Finally, there are a few events on the setting of the overall capin the system.

The selection of events is a crucial factor in event studies. As the baseline, Iuse all of the identified events, however, in Section 7, I study the sensitivity of theresults with respect to different event types in detail.

Carbon futures markets. Under the EU ETS, the right to emit a particularamount of greenhouse gases becomes a tradable commodity. The most liquidmarkets to trade these emission allowances are the futures markets at the EEXand the ICE. In this paper, I focus on data from the ICE, which has been found todominate the price discovery process in the European carbon market (Stefan andWellenreuther, 2020). The ICE EUA futures are listed on a quarterly expiry cycleand are traded up to 6 quarters out. The contract size is 1,000 EUAs and deliveryis physical.

3. High-frequency identification

Since policies to fight climate change are long-term in nature, they are likelyless subject to endogeneity concerns than other fiscal polices (Romer and Romer,2010). However, to properly address the concern that regulatory decisions in thecarbon market may take economic conditions into account, I implement a high-frequency identification approach.

The institutional framework of the European carbon market provides an idealsetting in this respect. First, as discussed above, there are frequent regulatoryupdates in the market that can have significant effects on the price of emissionallowances. Second, there exist liquid futures markets for trading emission al-lowances. This motivates the idea to construct a series of carbon policy surprisesby looking at how carbon prices change around regulatory events in the carbonmarket. By measuring the price change within a sufficiently tight window aroundthe regulatory news, it is possible to isolate the impact of the regulatory decision.Reverse causality of the state of the economy can be plausibly ruled out because

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it is known and priced prior to the decision and unlikely to change within thetight window.

To fix ideas, the carbon policy surprise series is computed by measuring thepercentage change in the EUA futures price on the day of the regulatory event tothe last trading day before the event:

CPSurpriset,d = Ft,d − Ft,d−1, (1)

where d and t indicate the day and the month of the event, respectively, and Ft,d

is the (log) settlement price of the EUA futures contract in month t on day d.Assuming that risk premia do not change over the narrow event window, we caninterpret the resulting surprise as a revision in carbon price expectations causedby the regulatory news.2

EUA futures are traded at different maturities. I focus here on the front con-tract (the contract with the closest expiry date), which is the most liquid. Im-portantly, near-dated contracts also tend to be less sensitive to risk premia thancontracts with longer maturities (Baumeister and Kilian, 2017; Nakamura andSteinsson, 2018). Thus, focusing on the front contract helps to further mitigateconcerns about time-varying risk premia.3

The daily surprises, CPSurpriset,d, are then aggregated to a monthly series,CPSurpriset, by summing over the daily surprises in a given month. In monthswithout any regulatory events, the series takes zero value.

The resulting carbon policy surprise series is shown in Figure 2. We can seethat regulatory news can have a substantial impact on carbon prices, with somenews moving prices in excess of 20 percent. In April 2007, for instance, when theCommission approved the NAPs of Austria and Hungary, carbon prices fell byaround 30 percent. Later in November, when the general court ruled on ex-postadjustments of Germany’s NAP, the carbon price rose by over 30 percent, eventhough prices were already at very low levels with the end of the pilot phase insight. Throughout the second phase, the regulatory surprises were a bit smaller,especially at the beginning. Towards the end, there were some larger surprises,for instance in November 2011 when a new regulation determining the volumeof allowances to be auctioned prior to 2013 came into force. Some very large

2While futures prices are in general subject to risk premia, there is evidence that these premiavary primarily at lower frequencies (Piazzesi and Swanson, 2008; Hamilton, 2009; Nakamura andSteinsson, 2018). If that is the case, risk premia are differenced out in the computation of the high-frequency surprise series.

3As shown in Appendix B.4, using contracts further out produces results that are at least qual-itatively similar. However, the first stage gets considerably weaker, further supporting the use ofthe front contract.

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Figure 2: The carbon policy surprise series

Notes: This figure shows the carbon policy surprise series, constructed by mea-suring the percentage change of the EUA futures price around regulatory pol-icy events concerning the supply of emission allowances in the European carbonmarket.

surprises occurred at the beginning of the third phase. On April 16, 2013 the Eu-ropean Parliament voted against the Commission’s back-loading proposal, whichled to a massive price fall of 43 percent. In September 2013, the Commission fi-nalized the free allocation to the industrial sector in phase three, which led to aprice increase of 10 percent. And in March 2014, the Commission approved twobatches of international credit entitlement tables, sending prices down by almost20 percent, just to name a few.

A crucial choice in high-frequency identification concerns the size of the eventwindow. There is a trade-off between capturing the entire response to the an-nouncement and the threat of other news confounding the response, so-calledbackground noise (cf. Nakamura and Steinsson, 2018). Because the exact releasetimes of the regulatory news detailed in Table A.1 are mostly unavailable, it ispractically infeasible to use an intraday window. However, to mitigate concernsabout background noise when using a daily window, I also present results froma heteroskedasticity-based approach that allows for background noise in the sur-prise series (see Section 7).

Finally, to be able to interpret the resulting series as a carbon policy surprises,it is crucial that the events do not release other information such as news aboutthe demand of emission allowances or economic activity in the EU more gen-erally. To address these concerns, I put great care in selecting regulatory updateevents that were about very specific changes to the supply of emission allowancesin the European carbon market and do not include broader events such as out-comes of Conference of the Parties (COP) meetings or other international confer-

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ences. Furthermore, I show that excluding the events regarding the overall cap,which are generally broader in scope, leads to very similar results. Likewise, ex-cluding events that overlap with broader news about the carbon market does notchange the results materially (see Section 7 for more details). Lastly, the focuson the supply of allowances is also confirmed by looking how some of the majorevents are received in the press.4

Diagnostics. To further assess the validity of the carbon policy surprise series, Iperform a number of diagnostic checks. Desirable properties of a surprise seriesare that it should not be autocorrelated, forecastable nor correlated with otherstructural shocks (see Ramey, 2016, for a detailed discussion).

Inspecting the autocorrelation function, I find little evidence for serial corre-lation. The p-value for the Q-statistic that all autocorrelations are zero is 0.92. Ialso find no evidence that macroeconomic or financial variables have any powerin forecasting the surprise series. For all variables considered, the p-values forthe Granger causality test are far above conventional significance levels, with thejoint test having a p-value of 0.99. I also show that the surprise series is uncor-related with other structural shock measures from the literature, including oil,uncertainty, financial, fiscal and monetary policy shocks. The corresponding fig-ures and tables can be found in Appendix B.1. Overall, this evidence supportsthe validity of the carbon policy surprise series.

4. Econometric approach

As illustrated above, the carbon policy surprise series has many desirable prop-erties. Nonetheless, it is only a partial measure of the shock of interest becauseit may not capture all relevant instances of regulatory news in the carbon mar-ket and could be measured with error (see Stock and Watson, 2018, for a detaileddiscussion of this point).

Thus, I do not use it as a direct shock measure but as an instrument. Providedthat the surprise series is correlated with the carbon policy shock but uncorre-lated with all other shocks, we can use it to estimate the dynamic causal effectsof a carbon policy shock. Because of the short sample at hand, I rely on VARtechniques for estimation. For identification, I use both an external instrument(Stock, 2008; Stock and Watson, 2012; Mertens and Ravn, 2013) and an internalinstrument approach (Ramey, 2011; Plagborg-Møller and Wolf, 2019). In the ex-

4See e.g. https://www.bbc.com/news/science-environment-22167675 or https://www.argusmedia.com/en/news/2234159-eu-eyes-42pc-lrf-extended-scope-for-ets.

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ternal instrument approach, the surprise series is used as an instrument externalto the VAR model. While this approach tends to be very efficient, it provides bi-ased estimates if the VAR is not invertible. In contrast, the internal instrumentapproach, which includes the instrument as the first variable in a recursive VAR,is robust to problems of non-invertibility.

An alternative approach would be to estimate the dynamic causal effects us-ing local projections (see Jordà, Schularick, and Taylor, 2015; Ramey and Zubairy,2018). However, this approach is quite demanding given the short sample, as itinvolves a distinct IV regression for each impulse horizon. Importantly, Plagborg-Møller and Wolf (2019) show that the internal instrument VAR and the LP-IV relyon the same invertibility-robust identifying restrictions and identify, in popula-tion, the same relative impulse responses. In Appendix B.2, I compare the LP-IVto the internal instrument VAR responses in the sample at hand. Reassuringly, theresponses turn out to be similar, even though the LP responses are more jaggedand less precisely estimated.

4.1. Framework

Consider the standard VAR model

yt = b + B1yt−1 + · · ·+ Bpyt−p + ut, (2)

where p is the lag order, yt is a n× 1 vector of endogenous variables, ut is a n× 1vector of reduced-form innovations with covariance matrix Var(ut) = Σ, b is an× 1 vector of constants, and B1, . . . , Bp are n× n coefficient matrices.

Under the assumption that the VAR is invertible, we can write the innovationsut as linear combinations of the structural shocks εt:

ut = Sεt. (3)

By definition, the structural shocks are mutually uncorrelated, i.e. Var(εt) = Ω isdiagonal. From the invertibility assumption (3), we get the standard covariancerestrictions Σ = SΩS′.

We are interested in characterizing the causal impact of a single shock. With-out loss of generality, let us denote the carbon policy shock as the first shock inthe VAR, ε1,t. Our aim is to identify the structural impact vector s1, which corre-sponds to the first column of S.

External instrument approach. Identification using external instruments worksas follows. Suppose there is an external instrument available, zt. In the applica-

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tion at hand, zt is the carbon policy surprise series. For zt to be a valid instrument,we need

E[ztε1,t] = α 6= 0 (4)

E[ztε2:n,t] = 0, (5)

where ε1,t is the carbon policy shock and ε2:n,t is a (n− 1)× 1 vector consistingof the other structural shocks. Assumption (4) is the relevance requirement andassumption (5) is the exogeneity condition. These assumptions, in combinationwith the invertibility requirement (3), identify s1 up to sign and scale:

s1 ∝E[ztut]

E[ztu1,t], (6)

provided that E[ztu1,t] 6= 0.5 To facilitate interpretation, we scale the structuralimpact vector such that a unit positive value of ε1,t has a unit positive effect ony1,t, i.e. s1,1 = 1. I implement the estimator with a 2SLS procedure and estimatethe coefficients above by regressing ut on u1,t using zt as the instrument. To con-duct inference, I employ a residual-based moving block bootstrap, as proposedby Jentsch and Lunsford (2019), and use Hall’s percentile interval to compute thebands.

Internal instrument approach. To assess potential problems of non-invertibility, I also employ an internal instrument approach. For identification,we have to assume in addition to (4)-(5) that the instrument is orthogonal toleads and lags of the structural shocks:

E[ztεt+j] = 0, for j 6= 0. (7)

In return, we can dispense of the invertibility assumption underlying equation(3).

Under these assumptions, we can estimate the dynamic causal effects byaugmenting the VAR with the instrument ordered first, yt = (zt, y′t)

′, andcomputing the impulse responses to the first orthogonalized innovation, s1 =

[chol(Σ)]·,1/[chol(Σ)]1,1. As Plagborg-Møller and Wolf (2019) show, this ap-proach consistently estimates the relative impulse responses even if the instru-ment is contaminated with measurement error or if the shock is non-invertible.

5To be more precise, the VAR does not have to be fully invertible for identification with externalinstruments. As Miranda-Agrippino and Ricco (2018) show, it suffices if the shock of interest isinvertible in combination with a limited lead-lag exogeneity condition.

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To conduct inference, I rely again on a residual-based moving block bootstrap.

4.2. Empirical specification

Studying the macroeconomic impact of carbon policy requires modeling the Eu-ropean economy and the carbon market jointly. The baseline specification con-sists of eight variables. For the carbon block, I use the energy component of theHICP as well as total GHG emissions.6 For the macroeconomic block, I includethe headline HICP, industrial production, the unemployment rate, the policy rate,a stock market index, as well as the real effective exchange rate (REER).7 More in-formation on the data and its sources can be found in Appendix A.2.

The sample spans the period from January 1999, when the euro was intro-duced, to December 2018. Recall, that the carbon policy surprise series is onlyavailable from 2005 when the carbon market was established. To deal with thisdiscrepancy, the missing values in the surprise series are censored to zero (seeNoh, 2019, for a theoretical justification of this approach). The motivation forusing a longer sample is to increase the precision of the estimates. However, re-stricting the sample to 2005-2018 produces very similar results.8

Following Sims, Stock, and Watson (1990), I estimate the VARs in levels. Apartfrom the unemployment and the policy rate, all variables enter in log-levels. Ascontrols I use six lags of all variables and in terms of deterministics only a con-stant term is included. However, the results turn out the be robust with respectto all of these choices (see Section 7).

5. The aggregate effects of carbon pricing

5.1. First stage

The main identifying assumption behind the (external) instrument approach isthat the instrument is correlated with the structural shock of interest but uncor-related with all other structural shocks. However, to be able to conduct standardinference, the instrument has to be sufficiently strong. To analyze whether this

6Unfortunately, GHG emissions are only available at the annual frequency. Therefore, I con-struct a monthly measure of emissions using the Chow-Lin temporal disaggregation method withindicators from Quilis’s (2020) code suite. As the relevant monthly indicators, I include the HICPenergy and industrial production. The results are robust to extending the list of indicators used.

7A delicate choice concerns the monetary policy indicator. As the baseline, I use the 3-monthEuribor. Using the shadow rate or longer-term government bond yields produces similar results.

8Note that while the carbon market was only established in 2005, the EU agreed to the Kyotoprotocol in 1997 and started planning on how to meet its emission targets shortly after. Thedirective for establishing the EU ETS came into force in October 2003 (Directive 2003/87/EC).

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is the case, I perform the weak instruments test by Montiel Olea and Pflueger(2013).

The heteroskedasticity-robust F-statistic in the first stage of the external in-strument VAR is 20.95. Assuming a worst-case bias of 20 percent with a sizeof 5 percent, the corresponding critical value is 15.06. As the test statistic liesclearly above the critical value, we conclude that the instrument appears to besufficiently strong to conduct standard inference.

5.2. The impact on emissions and the macroeconomy

Having established that the carbon policy surprise series is a strong instrument, Ipresent now the results from the external and internal instrument models. Figure3 shows the impulse responses to the identified carbon policy shock, normalizedto increase the HICP energy component by one percent on impact. Panel A de-picts the responses from the external instrument VAR and Panel B presents theresponses from the internal instrument model. I start by discussing the resultsfrom the external instrument approach.

A restrictive carbon policy shock leads to a strong, immediate increase in theenergy component of the HICP and a significant and persistent fall in GHG emis-sions. Thus, carbon pricing appears to be successful at reducing emissions andmitigating climate change. Turning to the macroeconomic variables, we can seethat the fall in emissions does not come without cost. Consumer prices, as mea-sured by the HICP, increase, industrial production falls, and the unemploymentrate rises significantly. The labor market response turns out to be particularlypronounced, consistent with reallocation frictions in the economy. However, thefall in activity and industrial production in particular appears to be less persistentthan the fall in emissions – implying an improvement in the emissions intensityin the longer run. While headline consumer prices increase persistently, the re-sponse of core HICP turns out to be more short-lived (see Appendix B.2 for moredetails). Monetary policy seems to largely look through the inflationary pressurescaused by the carbon policy shock, as reflected in the insignificant policy rate re-sponse. Stock prices fall significantly on impact but recover quite quickly andeven turn positive after about two years. Finally, the real exchange rate depreci-ates significantly.

In terms of magnitudes, a carbon policy shock increasing energy prices by 1percent causes a decrease in GHG emissions and industrial production by around0.5 percent, a rise in the unemployment rate of 0.2 percentage points and an in-crease in consumer prices of slightly more than 0.15 percent – measured at thepeak of the responses. Thus, the responses are not only statistically but also eco-

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Panel A: External instrument approach Panel B: Internal instrument approach

Figure 3: Impulse responses to a carbon policy shock

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICP energy by 1 percent on impact. The solid line is the pointestimate and the dark and light shaded areas are 68 and 90 percent confidence bands, respectively.

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nomically significant.

The results from the internal instrument model turn out to be very similar.The signs are all consistent and the responses are also similar in shape. The maindifference lies in the response of energy prices, which turns out to be strongerand more persistent than in the external instrument model. Consequently, themagnitudes for emissions and the economic variables also turn out to be larger.It should be noted, however, that the responses are also less precisely estimated.Overall, these findings suggest that the results are robust to relaxing the assump-tion of invertibility. In the remainder of the paper, I thus use the external instru-ments model as the baseline.

By way of summary, these findings clearly illustrate the policy trade-off be-tween reducing emissions and thus the future costs of climate change and thecurrent economic costs associated with climate change mitigation policies. Myresults also point to a strong pass-trough of carbon to energy prices, as can beseen from the significant energy price response. Unfortunately, it is not possi-ble to quantify the pass-through directly, as my baseline specification does notinclude the carbon price, which only became available in 2005 when the carbonmarket was established. However, estimates from a model including the carbonprice, estimated on the shorter sample, point to a pass-through of around 20 per-cent at its peak (see Appendix B.2).

5.3. Historical importance

In the previous section, we have seen that carbon policy shocks can have sig-nificant effects on emissions and the economy. An equally important question,however, is how much of the historical variation in the variables of interest cancarbon policy account for? To this end, I perform a historical decomposition ex-ercise. To get a better idea of the average contribution, I also perform a variancedecomposition in Appendix B.2.

Figure 4 shows the historical contribution of carbon policy shocks to energyprice inflation and GHG emissions growth. We can see that carbon policy shockshave contributed meaningfully to variations in energy prices and GHG emissionsin many episodes. On average, carbon policy shocks account for about a third ofthe variations in energy prices and a quarter of the variations in emissions athorizons up to one year. Furthermore, carbon policy shocks can also explain anon-negligible share of the variations in other macroeconomic and financial vari-ables (see Appendix B.2). Importantly, we can also see that the significant fallin emissions in the aftermath of the global financial crisis was not driven by car-

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bon policy shocks. This result is reassuring that the high-frequency identificationstrategy is working as the fall in emissions during the Great Recession was clearlydriven by lower demand and not supply-specific factors in the European carbonmarket.

Panel A: HICP energy inflation

Panel B: GHG emissions growth

Figure 4: Historical decomposition of energy inflation and emissions growth

Notes: The figure shows the cumulative historical contribution of carbon policy shocksover the estimation sample for a selection of variables against the actual evolution ofthese variables. Panel A shows the historical contribution to HICP energy inflation, PanelB presents the contribution to GHG emissions growth. The solid line is the point estimateand the dark and light shaded areas are 68 and 90 percent confidence bands, respectively.

5.4. Propagation channels

Having established that carbon policy shocks are an important driver of the econ-omy, we now analyze in more detail the underlying transmission channels.

The role of energy prices. The above results suggest that energy prices play acrucial role in the transmission of carbon policy shocks. Power producers seem to

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pass through the emission costs to energy prices to a significant extent, which is inline with previous empirical evidence (see e.g. Veith, Werner, and Zimmermann,2009; Bushnell, Chong, and Mansur, 2013). To further corroborate this channel, Iperform an event study using daily stock market data. More specifically, I mapout the effects of carbon policy surprises on carbon futures and stock prices byrunning the following set of local projections:

qi,d+h − qi,d−1 = βi0 + ψi

hCPSurprised + βih,1∆qi,d−1 + . . . + βi

h,p∆qi,d−p + ξi,d,h,

(8)

where qi,d+h is the (log) price of asset i after h days following the event d,CPSurprised is the carbon policy surprise on event day. ψi

h measures the effect onasset price i at horizon h. For inference, I follow the lag-augmentation approachproposed by Montiel Olea and Plagborg-Møller (2020). In particular, I augmentthe controls by an additional lag and use heteroskedasticity-robust standard er-rors.

Figure 5: Carbon prices and stock market indicesNotes: Responses of carbon futures prices and stock indices for the market and the utilitysector to a carbon policy surprise. The sample spans the period from April 22, 2005 toDecember 31, 2018. As controls, I use 15 lags of the respective dependent variable.

The results are shown in Figure 5. We can see that carbon policy surpriseslead to a significant increase in carbon futures prices. The front contract increasessignificantly for about three weeks. The effect turns out to be quite persistent

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as the price of the second contract, which expires in the following quarter, alsoincreases significantly. Turning to the stock market, we can see that the marketdoes not seem to move immediately following carbon surprises. Only after aboutone week, the index starts to fall significantly. This may reflect the fact that theEU ETS is a relatively new market and thus market participants need some timeto process the regulatory news. Looking into potential sectoral heterogeneities,I find that most sectors display a similar response to the market. Among the 11GICS sectors, utilities is the only sector that stands out, displaying a significantincrease in stock prices.

These results suggest that the European utility sector is able to profit, at leastin the short run, from a more stringent carbon pricing regime. This findingis in line with previous empirical evidence (Veith, Werner, and Zimmermann,2009; Bushnell, Chong, and Mansur, 2013) and may be explained as follows. Theutility sector is segmented due to the structure of existing transmission networks,which substantially limits import penetration from countries without a carbonprice. Thus, utility companies are able to increase their product prices withoutlosing market share. At the same time, utilities can decarbonize at relativelylow cost, for instance by switching from coal to gas-fired electricity, and sell theexcess allowances at a profit. In contrast, for industrial emitters competing ininternational product markets, passing through the cost of carbon could lead tosignificant losses in market share, and decarbonizing tends to be more costly.

The transmission to the macroeconomy. To better understand how carbon pric-ing and the associated increase in energy prices affect the economy, I study theresponses of a selection of financial and macroeconomic variables. To be able toestimate the dynamic causal effects on these variables, I extract the carbon pol-icy shock from the monthly VAR as CPShockt = s′1Σ−1ut (for a derivation, seeStock and Watson, 2018) and estimate the dynamic causal effects using simplelocal projections:

yi,t+h = βi0 + ψi

hCPShockt + βih,1yi,t−1 + . . . + βi

h,pyi,t−p + ξi,t,h, (9)

where ψih is the effect on variable i at horizon h. Importantly, we can also use this

approach to estimate the effects on variables that are only available at the quar-terly or even annual frequency. In this case, we aggregate the shock CPShockt bysumming over the respective months before running the local projections. Usingthe shock series directly in the local projections as opposed to the high-frequencysurprises increases the statistical power of these regressions, as the shock seriesis consistently observed and spans the entire sample. Note, however, that this

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comes at the cost of assuming invertibility. Throughout the paper, I normalize theshock to increase the HICP energy component by one percent on impact. The con-fidence bands are again computed using the lag-augmentation approach (MontielOlea and Plagborg-Møller, 2020).9

Increases in energy prices can have significant effects on the macroeconomy(see e.g. Hamilton, 2008; Edelstein and Kilian, 2009). They directly affect house-holds and firms by reducing their disposable income. Given that energy de-mand is considered to be quite inelastic, consumers and firms have less moneyto spend and invest after paying their energy bills (and financing their emissionallowances). Note, however, that the magnitude of this discretionary income ef-fect is bounded by the energy share in expenditure, which is around 7 percent inEurope. In addition, increased uncertainty about future energy prices may leadto a further fall in spending and investment because of precautionary motives.

Energy prices also affect the economy indirectly through the general equilib-rium responses of prices and wages and hence of income and employment. Aftera carbon policy shock increasing energy prices, the direct decrease in households’and firms’ consumption and investment expenditure will lead to lower outputand exert downward pressure on employment and wages. The additional fall inaggregate demand induced by lower employment and wages lies at the core ofthe indirect effect.

To shed light on the different transmission channels at work, I study the re-sponses of GDP and its components in Figure 6. We can see that the shock leadsto a significant fall in real GDP. The response looks quite similar to the response ofindustrial production, both in terms of shape and magnitude. Looking at the dif-ferent components, we can see that the shock leads to a significant and persistentfall in consumption. Investment, as measured by gross fixed capital formation,also falls significantly but the response turns out to be somewhat less persistent.Finally, net exports, expressed as a share of GDP, increase significantly, in linewith the real depreciation of the euro. Inspecting the responses of exports andimports separately reveals that both exports and imports fall but imports fall bymuch more causing the significant increase in net exports.

Importantly, the magnitudes of the effects are by an order of magnitude largerthan what can be accounted for by the direct effect through higher energy prices.This suggests that indirect effects play a crucial role in the transmission of carbonpolicy shocks. In Section 6, I shed more light on the role of different transmission

9Reassuringly, the comparison of the internal and external instrument models as well as therobustness checks in Section 7 did not point to any problems of non-invertibilty. As controls inthe local projections, I use 7 lags for monthly variables, 3 lags for quarterly variables and 2 lagsfor annual variables.

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Figure 6: Effect on GDP and components

Notes: Impulse responses of real GDP, consumption, investment and net exports ex-pressed as a share of GDP.

channels using detailed household micro data.The above results support the notion that higher energy prices and the asso-

ciated direct and indirect effects are a dominant transmission channel of carbonpricing. However, apart from the effects through energy prices, carbon pricingmay also affect the economy through other channels, for instance by affectingfinancing conditions or increased uncertainty. It turns out, however, that thesevariables respond to carbon policy shocks only with a lag, similar to stock prices,and the responses do not turn out to be very significant (see Figure B.5 in the Ap-pendix). Thus, these alternative channels are unlikely to play a dominant role inthe transmission of carbon policy shocks.

The effect on innovation. We have seen that carbon pricing is successful in re-ducing emissions but this comes at an economic cost, at least in the short term.However, there could also be positive effects in the longer term, for instance byspurring innovation in low-carbon technologies. In fact, part of the vision for theEU ETS is to promote investment in clean, low-carbon technologies (EuropeanComission, 2020a).

To analyze this channel in more detail, I study how the patenting activity inclimate change mitigation technologies is affected by the carbon policy shock.The European Patent Office (EPO) has developed specific classification tags forclimate change mitigation technologies.

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Figure 7: Patenting in climate change mitigation technologies

Notes: Impulse responses of patenting activity in climate change mitigation technologies.Depicted is the response of the number of climate change mitigation patent filings, inabsolute terms (left panel) and as a share of all patents filed at the EPO (right panel).

The results are shown in Figure 7. We can see that the shock leads to a signifi-cant increase in low-carbon patenting, both in absolute terms and also relativeto the overall patenting activity. Thus, carbon pricing appears to be success-ful in stimulating innovation in climate change mitigation technologies. Theseresults support the findings of Calel and Dechezleprêtre (2016), who employ aquasi-experimental design exploiting inclusion criteria at the installations levelto estimate the ETS system’s causal impact on firms’ patenting, and also chimewell with the previously documented stock market response, which reboundsand even turns positive in the longer run.

6. The heterogeneous effects of carbon pricing

Recently, there has been a big debate in Europe on energy poverty and the dis-tributional effects of carbon pricing amid the European Commission’s plans ofextending the carbon market to buildings and transportation (European Comis-sion, 2021). While the commission did propose a Social Climate Fund to cushionthe adverse effects on vulnerable households, several observers have argued thatthe proposal does not do enough to ensure a fair and equitable transition.10

Against this backdrop, it is crucial to better understand the distributional im-pact of the EU ETS. If certain groups are left behind, this could ultimately under-mine the success of climate policy. To this end, I study the heterogeneous effectsof carbon pricing on households. This will help to get a better picture on howcarbon pricing affects economic inequality. Furthermore, looking into potentialheterogeneities in the consumption responses can help to better understand the

10See e.g. https://righttoenergy.org/2021/07/14/fit-for-55-not-fit-for-europes-energy-poor/.

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transmission channels at work. There is reason to believe that there are impor-tant heterogeneities at play. First, the direct effect through energy prices cruciallydepends on the energy expenditure share, which is highly heterogeneous acrosshouseholds. Second, the indirect effects will also be heterogeneous to the extentthat individual incomes respond differently to the change in aggregate expendi-ture, for instance because of differences in the income composition or the sectorof employment. As poorer households tend to have a higher energy share andtheir income tends to be more cyclical, we expect the impact to be regressive.

6.1. Household survey data

To be able to analyze the heterogeneous effects of carbon policy shocks on house-holds, we need detailed micro data on consumption expenditure and income ata regular frequency for a sample spanning the last two decades. Unfortunately,such data does not exist for most European countries let alone at the EU level.Therefore, I focus here on the UK which is one of the few countries that has suchdata as part of the Living Costs and Food Survey (LCFS).11

The LCFS is the most significant survey on household spending in the UK andprovides high-quality, detailed information on expenditure, income, and house-hold characteristics. The survey is fielded in annual waves with interviews beingconducted throughout the year and across the whole of the UK. I compile a re-peated cross-section based on the last 20 waves, spanning the period 1999 to 2018.Each wave contains around 6,000 households, generating over 120,000 observa-tions in total. To compute measures of income and expenditure, I first express thevariables in per capita terms by dividing household variables by the number ofhousehold members. In a next step, I deflate the variables by the (harmonized)consumer price index to express them in real terms. For more information, seeAppendix A.3.

Ideally, we would like to observe how individual consumption expenditureand income evolve over time. Unfortunately, the LCFS being a repeated cross-section has no such panel dimension. To construct a pseudo-panel, it is commonto use a grouping estimator in the spirit of Browning, Deaton, and Irish (1985).

A natural dimension for grouping households is their income. However, asthe income may endogenously respond to the shock of interest, we cannot use thecurrent household income as the grouping variable. Luckily, the LCFS does not

11The UK was part of the EU ETS until the end of 2020. Over the sample of interest, the ag-gregate effects in the UK are comparable to the ones documented at the EU level, see Figure B.6in the Appendix. To further mitigate concerns about external validity, I show that the results forother European countries such as Denmark and Spain are very similar, see Figure B.26.

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only collect information about current household income but also about normalhousehold income, which should by construction not be affected by temporaryshocks.12 Thus, I use the normal disposable household income to group house-holds into three pseudo-cohorts: low-income, middle-income, and high-incomehouseholds.13 Following Cloyne and Surico (2017), I assign each household to aquarter based on the date of the interview, and create the group status as the bot-tom 25 percent of the normal disposable income distribution for low-income, themiddle 50 percent for middle-income, and the top 25 percent for high-income inevery quarter of a given year. The individual variables are then aggregated usingsurvey weights to ensure representativeness of the British population.

Table 1 presents some descriptive statistics, unconditional for all householdsas well as by conditioning on the three income groups. We can see that weeklytotal expenditure (excl. housing) and housing expenditure are both increasing inincome. While low-income households spend a large part of their budget on non-durables, richer households spend more on services and durables. Importantly,poorer households spend a significantly higher share of their expenditure on en-ergy: the (average) energy share stands at close to 9.5 percent for low-income, justabove 7 percent for middle income, and around 5 percent for high-income house-holds. Thus, to the extent that energy demand is inelastic, poorer households aremore exposed to increases in energy prices.

The different income groups turn out to be comparable in terms of their age.This can be seen from the median age which is around 50 for all groups and alsofrom Figure B.8 in the Appendix, which shows that the empirical age distributionis similar across all three income groups. As expected, high-income householdstend to be more educated, as can be seen from the larger share of households thathave completed post-compulsory education. Finally, higher-income householdstend to be homeowners, either by mortgage or outright, while among the low-income there is a large share of social renters. Importantly, all these variablesare rather slow-moving and unlikely to confound potential heterogenities in thehousehold responses to carbon policy shocks, which exploit variation at a muchhigher frequency (see Figure B.9 in the Appendix).

12While it may be affected by permanent shocks, this should not be too much of a concern forour grouping strategy as the normal income variable is very slow moving. I have also verifiedthat normal income does not respond significantly to the carbon policy shock. In contrast, currentincome falls significantly and persistently, as shown in Figure B.10 in the Appendix.

13In Appendix B.3, I use a selection of other proxies for the income level, including earnings,expenditure, and an estimate for permanent income obtained from a Mincerian-type regression.The results turn out to be robust to using these alternative measures of income for grouping.Alternatively, I tried to group households by their energy share directly. The results turn outagain to be very similar, see Figure B.21. This suggests that the energy share is a good proxy forthe level of income, with poorer households having higher energy shares (see also Table B.4).

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Table 1: Descriptive statistics on households in the LCFS

Overall By income group

Low-income Middle-income High-income

Income and expenditureNormal disposable income 236.3 112.6 236.3 466.6Total expenditure (excl. housing) 157.3 91.6 155.4 269.6

Energy share 7.2 9.4 7.1 5.1Non-durables (excl. energy) share 49.6 55.0 49.7 44.1Services share 31.9 26.7 31.9 37.2Durables share 11.3 8.9 11.3 13.6

Housing 32.0 18.8 31.1 58.0

Household characteristicsAge 51 46 54 49Education (share with post-comp.) 33.5 25.0 29.1 51.0Housing tenure

Social renters 20.9 47.1 17.4 3.7Mortgagors 42.6 25.5 41.6 60.4Outright owners 36.6 27.4 41.0 36.0

Notes: The table shows descriptive statistics on weekly per capita income and expen-diture (in 2015 pounds), the breakdown of expenditure into energy, non-durables excl.energy, services and durables (as a share of total expenditure) as well as a selection ofhousehold characteristics, both over all households and by income group. For variablesin levels such as income, expenditure and age the median is shown while the shares arecomputed based on the mean of the corresponding variable. Note that the expenditureshares are expressed as a share of total expenditure excl. housing and thus services do notinclude housing either, and semi-durables are subsumed under the non-durable category.Age corresponds to the age of the household reference person and education is proxiedby whether a member of a household has completed a post-compulsory education.

6.2. Median effect and the response of inequality

We are now in a position to study how households’ expenditure and income re-spond to carbon policy shocks.14 As a validating exercise, we first look at themedian household expenditure response and compare it to the consumption re-sponse based on national statistics. As can be seen from the left panel of Figure 8,the median response aligns quite well with the response from national statistics,both in terms of shape and magnitude (see Figure 6).

14In the LCFS, households interviewed at time t are typically asked to report expenditure overthe previous three months (with the exception of non-durable consumption which refers to theprevious two weeks). To eliminate some of the noise inherent in survey data, I smooth the ex-penditure and income measures with a backward-looking (current and previous three quarters)moving average, as in Cloyne, Ferreira, and Surico (2020). Similar results are obtained when us-ing the raw series instead (even though the responses become more jagged and imprecise) or byusing smooth local projections as proposed by Barnichon and Brownlees (2019), see Figure B.14in the Appendix. To account for potential seasonal patterns I include a set of quarterly dummiesas controls, following again Cloyne, Ferreira, and Surico (2020).

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Figure 8: Response of household consumption expenditure

Notes: Impulse responses of total expenditure excluding housing. The left panel showsthe median response and the right panel shows the response of consumption inequality,as measured by the Gini coefficient.

To investigate into potential heterogeneities, we also look at the Gini index forhousehold expenditure. The response is shown in the right panel of Figure 8. Wecan see that the shock leads to a significant increase in inequality, especially atlonger horizons. While this result is interesting in itself, it does not tell us whichgroups are more hardly affected than others.

6.3. Heterogeneity by household income

Having analyzed the aggregate effects as well as the effects on inequality, wenow look into the underlying heterogeneity by income group. Figure 9 showsthe responses of household expenditure and current income for the three incomegroups we consider.

We can see that there is pervasive heterogeneity in the expenditure responsebetween income groups. Low-income households reduce their expenditure sig-nificantly and persistently. In contrast, the expenditure response of higher-income households is rather short-lived and only barely statistically significant.Interestingly, the income responses turn out to be somewhat more homogeneous.While low-income households experience the largest drop in income, higher-income households also experience a non-negligible income decline, even thoughit turns out to be less persistent.15 The finding that the expenditure of high-income households does nevertheless not respond significantly points to the factthat these households have more savings and liquid assets to smooth the tempo-rary fall in their income. In contrast, the low-income households are hit twofold.

15While the income decline of the low- and middle-income households appears to be driven bya fall in earnings, high-income households also experience a fall in their financial income, whichthen however reverses and turns significantly positive – in line with the stock market response,see Figure B.15 in the Appendix.

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Figure 9: Household expenditure and income responses by income groups

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income for low-income (bottom 25 percent), middle-income (middle50 percent) and high-income households (top 25 percent). The households are groupedby total normal disposable income and the responses are computed based on the medianof the respective group.

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First, they spend a larger share of their budget on energy and are thus, as energyexpenditure is highly inelastic, adversely affected by the higher energy bill. Sec-ond, they experience a larger fall in income, as they tend to work in sectors thatare more hardly affected by the carbon policy shock (see Section 6.4). At the sametime, they are more likely to be financially constrained and less able to cope withthe adverse effects on their income and budget.

At this stage, it is worth discussing a potential concern about grouping house-holds concerning selection. The assignments into the income groups are notrandom and some other characteristics may, potentially, be responsible for theheterogeneous responses I document. To mitigate these concerns, I group thehouseholds by a selection of other grouping variables, including age, educationand housing tenure. The results are shown in Figures B.16-B.18 in the Appendix.While there is not much heterogeneity by age, less educated households tendto respond more than better educated ones and social renters tend to respondmore than homeowners. However, none of the alternative grouping variablescan account for the patterns uncovered for income, suggesting that we are notspuriously picking up differences in other household characteristics.

6.4. Direct versus indirect effects

While the expenditure responses are, as expected, more pronounced the higherthe energy share, the magnitudes are much larger than what can be accounted forby the discretionary income effect alone. Assuming that energy demand is com-pletely inelastic, the direct effect is bounded by the energy share of the respectivegroup.16 However, the peak response of low-income households is around one– close to ten times the energy share of that group. This suggests that indirect,general equilibrium effects via income and employment account for a large partof the overall effect on household expenditure; a finding that is also supportedby the significant effects on unemployment documented in Section 5.2.

To shed more light on these indirect effects, I study how the income responsevaries by the sector of employment using data from the UK Labour Force Survey(LFS).17 I consider two dimensions to group sectors. First, I group sectors by

16Energy expenditure does indeed turn out to be pretty inelastic, especially for low-incomehouseholds, see Figures B.19-B.20 in the Appendix. While the energy share of higher-incomehouseholds does not respond significantly, the energy share of low-income households tends toincrease – reflecting the fact that their energy expenditure hardly changes while their total con-sumption expenditure falls significantly.

17Unfortunately, the LCFS does not include any information on the sector of employment.Therefore, I use data from the LFS which provides detailed information on employment sectorand income. For more information on the LFS, see Appendix A.3.

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their energy intensity to gauge the role of the conventional cost channel. Second,I group sectors by how sensitive they are to changes in aggregate demand (seeAppendix B.3 for more information).

Table 2: Sectoral distribution of employment

Sectors Overall By income group

Low-income Middle-income High-income

Energy intensityHigh 21.8 9.8 25.8 25.9Lower 78.2 90.2 74.2 74.1

Demand sensitivityHigh 30.6 49.1 27.3 18.1Lower 69.4 50.9 72.7 81.9

Notes: The table depicts the sectoral employment distribution of households in the LFS,both overall and by income group (where income is proxied by net pay in the main andsecond job). I group sectors along two dimensions: their energy intensity and their de-mand sensitivity. The energy-intensive sectors include agriculture, utilities, transporta-tion, and manufacturing (SIC sections A–E and I). The demand-sensitive sectors includeconstruction, wholesale and retail trade, hospitality, and entertainment and recreation(SIC sections F–H and O–Q).

Table 2 presents descriptive statistics on the sectoral distribution of house-holds, both overall and by income group. We can see that only few low-incomehouseholds work in sectors with a high energy intensity such as utilities or man-ufacturing. Thus, the sectors’ energy intensity is unlikely to explain the hetero-geneous income responses that we observe. A more relevant dimension of het-erogeneity appears to be the sectors’ demand sensitivity: low-income householdswork disproportionally in sectors that tend to be more sensitive to aggregate de-mand fluctuations, such as retail or hospitality, while a large majority of higherincome households work in less demand-sensitive sectors.

In a next step, I study how the median income across different sectors changesafter a carbon policy shock. Figure 10 presents the results. It turns out that the sec-tors’ energy intensity does not appear to play a crucial role for the magnitude ofthe income response. In fact, the response in sectors with a high energy intensityis relatively comparable to the response in sectors with a lower energy intensity.18

In contrast, there is significant heterogeneity by the sectors’ demand-sensitivity:

18Note that I exclude utilities from the energy-intensive group, as there is reason to believethat the utility sector behaves differently from other energy-intensive sectors. In fact, as shownin Figure B.22 in the Appendix, the utility sector does not display a significant fall in incomes, inline with the findings from Section 5.4.

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Figure 10: Income response by sector of employment

Notes: Impulse responses of income (pay from main and second job net of deduc-tions and benefits) in different sectors, grouped by their energy-intensity and demand-sensitivity. The response is computed based on the median income in the respectivegroup of sectors. The sector groups are described in detail in Table 2.

households working in demand-sensitive sectors experience the largest and mostsignificant fall in their income after a carbon policy shock while households inless-demand sensitive sectors face a much more muted income response.

These results support the interpretation that carbon policy shocks mainlytransmit to the economy through the demand side, and not by affecting produc-tion costs. While this may seem surprising, it is in line with previous evidence byKilian and Park (2009) on the transmission of energy price shocks. Importantly,the results also help explain why low-income households display a stronger fallin their income, as they disproportionally work in demand-sensitive sectors. Inresponse to a carbon policy shock, these sectors face a stronger decrease in de-mand than other sectors and thus react by laying off employees and cutting com-pensation.

To better disentangle these indirect effects from the direct effect via the energyshare, I look at the responses of low- and higher-income households condition-ing on the most exposed high-energy share households and households with alower energy share. The responses are shown in Figure B.23 in the Appendix. Afew observations emerge from this exercise. First, we can see that low-incomehouseholds with a high energy share display a much stronger fall in their ex-

32

penditure than households with a lower energy share in the same income group.This differential response, however, cannot be solely accounted for by the energyshare heterogeneity as the income response also turns out to be more pronouncedfor low-income households with a high energy share. The role of these indirecteffects via the decrease in household income can also be appreciated by compar-ing the responses of low-income and higher-income households conditional ona high energy share. Despite having a comparable energy share, higher-incomehouseholds lower their expenditure by much less, consistent with the fact thatthey experience a smaller fall in their incomes. Interestingly, there is less hetero-geneity in the expenditure response across income groups conditional on a lowerenergy share, consistent with the fact that the income responses in this case arealso more similar. Overall, these results further illustrate the importance of indi-rect effects working through income and employment.

Apart from the direct effect on households’ discretionary income, there mayalso be other direct effects at play. For instance, households may postpone pur-chases of certain durable goods in light of increased uncertainty or there may bea shift in expenditure on durables that are complementary in use with energy(see also Edelstein and Kilian, 2009). However, given the muted response of un-certainty indicators (see Section 5.4) and the relatively small share of durable ex-penditure, these channels do likely not play a dominant role in the transmissionof carbon policy shocks. In fact, as shown in Figures B.24-B.25 in the Appendix,durable expenditures fall but the response turns out to be rather short-lived andcan thus not account for the persistent effects observed for total expenditure.

6.5. Policy implications

We have documented substantial heterogeneity in the response of households tocarbon policy shocks. The findings illustrate that the economic costs of carbonpricing are not borne equally across society. It is the lower-income income house-holds that are the most hardly affected, having to reduce their expenditures themost, and that are driving the aggregate response. In fact, the overall poundchange in expenditure over the five-year period following a carbon policy shockis −£329.9 for low-income, −£183.4 for middle-income, and −£162.2 for high-income households.19 These heterogeneities are striking against the backdropthat low-income households have much lower levels of expenditure to start with,as shown in Table 1. Put differently, low-income households account for about 40

19To compute the overall pound change over the impulse horizon, I compute the present dis-counted value of the impulse response, using the average real interest rate over the sample of in-terest, and multiplying this value by the median quarterly expenditure for each group.

33

percent of the aggregate effect of carbon pricing on consumption, despite the factthat they only represent 25 percent of the population.

The results also highlight the importance of energy prices in the transmissionof carbon policy shocks through direct and indirect channels that disproportion-ally affect lower-income households – the very households that also tend to befinancially constrained and have a higher marginal propensity to consume. Myfindings suggest that fiscal policies targeted to the most affected households canreduce the economic costs of climate change mitigation policies and amelioratethe trade-off between reducing emissions and maintaining economic activity. Tothe extent that energy demand is inelastic, which turns out to be particularly thecase for low-income households, this should not compromise the reductions inemissions.

Such a policy could be implemented for instance by recycling some of the rev-enues generated from auctioning allowances. While in the first two phases ofthe ETS, the majority of allowances was freely allocated, auctioning became thedefault in the third phase, generating substantial auction revenues. For the pe-riod from 2012 to June 2020, the total revenues generated by the member statesof the EU ETS exceeded 57 billion euros (European Comission, 2020b). In the ETSdirective from 2008, the member states agreed that at least half of the auctionrevenues should be used for climate and energy related purposes, both domesticand internationally. Indeed, over the period 2013-2019, close to 80 percent of auc-tion revenues were used for such purposes, with many countries using all of therevenues for climate action. While this should help to further propel emission re-ductions, my results indicate that by redistributing part of the auction revenues tothe most hardly affected groups in society, it is possible to offset the distributionaleffects and reduce the economic costs of climate change mitigation policies.20

The above intuition is confirmed in a New Keynesian model with a climateblock in the spirit of Golosov et al. (2014), featuring heterogeneity in households’energy expenditure shares, income incidence and marginal propensities to con-sume (MPCs). Calibrated to match key empirical moments from macro and mi-cro data, the model suggests that redistributing carbon revenues to high MPChouseholds can mitigate the effect on aggregate consumption by around 40 per-cent while reducing inequality at the same time. The model also illustrates that

20The current ETS does not feature such a direct redistribution scheme, however, there are cer-tain other, indirect solidarity measures in place, e.g. via the Cohesion Fund, the Just TransitionFund and the European Social Fund Plus. Only in the recent ‘Fit for 55’ plan, the European Comis-sion takes a step in the direction of redistributing revenues, proposing a new Social Climate Fund.However, the proposed fund will be limited to the new emissions trading system for building andtransport fuels, and only includes an amount equivalent to 25 percent of the expected revenues.

34

household heterogeneity plays a crucial role in the transmission of carbon policyshocks and is key to reconcile the large effects observed in the data (see AppendixD for a detailed description of the model and extended discussion of the results).

These results speak directly to the recent debate on carbon pricing and in-equality in Europe. Another important argument for cushioning the distribu-tional impact is that a successful transition to a low-carbon economy requirespublic support. If certain groups feel left behind, this could undermine the suc-cess of climate policy as the yellow vest movement in France, which started asa demonstration against higher fuel taxes, has shown for instance (see also Knit-tel, 2014). Indeed, in Appendix B.3 I show that carbon policy shocks lead to adecrease in the public support of climate policy. While the support among low-income households falls significantly and persistently, the response of higher-income households is more short-lived and even turns positive at longer hori-zons. These results suggest that compensating low-income households that aremore exposed to carbon pricing may indeed help to increase the public supportof climate change mitigation policies – consistent with recent evidence by Ander-son, Marinescu, and Shor (2019).

7. Sensitivity analysis

In this section, I perform a number of robustness checks on the identificationstrategy and the model specification used to isolate the carbon policy shock. Themain results of these checks are summarized below. More information as well asthe corresponding figures and tables can be found in Appendix B.4.21

Selection of relevant events. A crucial choice in the high-frequency event studyapproach concerns the selection of relevant events. For the exclusion restrictionto be satisfied, the events should only release information about the supply ofemission allowances and not about other factors such as economic activity. Tothis end, I have not included broader events such as the Paris agreement or otherCOP meetings but limited the analysis to specific events in the European carbonmarket. The most obvious candidates are events about the free allocation andauctioning of emission allowances. I have also included events on the overall capin the carbon market as well as events about international credits.

Because the events concerning the cap tend to be broader in nature, I excludethese events as a robustness check. As shown in Figure B.29, the results turn out

21I focus here on the external instrument VAR for the robustness checks. The results for theinternal instrument approach are available upon request.

35

to be robust. I have also tried to exclude the events about international credits,which affect the supply of allowances only indirectly, by changing the number ofcredits from international projects that can be exchanged for allowances. FromFigure B.30, we can see that the results turn out to be very similar. By goingthrough all events in detail, I could also identify some events that are poten-tially confounded, either because some other event happened on the same day(more on this below) or because they could potentially also contain some infor-mation about demand in the carbon market. Reassuringly, however, excludingthese events does not change the results materially (see Figure B.32). Finally, Ihave verified that the identification strategy does not hinge upon extreme events.Excluding the largest surprises (price change in excess of 30 percent) does notchange the results materially, even though the responses are less precisely esti-mated (see Figure B.33).

Confounding news. Another important choice in high-frequency identificationconcerns the size of the event window. As discussed in Section 3, there is a trade-off between capturing the entire response to the policy news and backgroundnoise, i.e. the threat of other news confounding the response. Common windowchoices range from 30-minutes to multiple days. Unfortunately, the exact releasetimes are unavailable for the majority of the policy events considered, making itinfeasible to use an intraday window. Therefore, I use a daily window to computethe policy surprises.

To mitigate concerns about other news confounding the carbon policy sur-prise series, I employ an alternative identification strategy exploiting the het-eroskedasticity in the data (Rigobon, 2003; Nakamura and Steinsson, 2018). Theidea is to clean out the background noise in the surprise series by compar-ing movements in carbon prices during policy event windows to other equallylong and otherwise similar event windows that do not contain a regulatory up-date event. In particular, I use the changes in carbon futures prices on thesame weekday and week in the months prior a given regulatory event. Anoverview of announcement and control dates can be found in Table B.6 in theAppendix. More details on the underlying assumptions and how to implementthe heteroskedasticity-based approach are provided in Appendix C.

Figure B.34 shows the carbon policy surprise series together with the controlseries. We can see that the policy surprise series is over six times more volatilethan the control series. It is exactly this shift in variance that can be exploited foridentification, assuming that the shift is driven by the carbon policy shock. Fig-ure B.35 shows the impulse responses estimated from this alternative approach.

36

The results turn out to be consistent with the baseline results from the external in-strument approach, even though the responses turn out to be a bit less preciselyestimated. These results suggest that the bias induced by background noise islikely negligible in the present application.

Sample and specification choices. An important robustness check concerns theestimation sample. Recall, that the baseline sample goes back to 1999, which islonger than the instrument sample which only starts in 2005. The main moti-vation for using the longer sample is to increase the precision of the estimates.As a robustness check, I restrict the overall sample to the 2005-2018 period. Theresponses are shown in Figure B.37. Overall, the results are very similar to theones using the longer sample. However, some responses turn out to be a bit lessstable, which could point to difficulties in estimating the model dynamics on therelatively short sample.

Another interesting check concerns the sample for the carbon policy surprises.Recall that the EU ETS was established in phases and the first phase was a pilotphase. As a robustness test, I exclude the regulatory news from this first phase.From Figure B.38, we can see that the point estimates turn out to be quite similar.However, as probably had to be expected the responses are much less impreciselyestimated. This illustrates nicely how the identification strategy leverages the factthat establishing the carbon market was a learning-by-doing process where therules have been continuously updated.

I also perform a number of sensitivity checks on the specification of the model.The baseline VAR includes 8 variables, which is relatively large, especially againstthe backdrop of the short sample. As a robustness test, I use a 6-variable model,excluding stock prices and the real exchange rate. As can be seen from FigureB.39, the results from this smaller model turn out to be very similar to the largerbaseline model. The results also turn out to be robust to the lag order (FiguresB.41-B.42 show the responses using 3 or 9 lags) and the choice of deterministics(Figure B.40 includes a linear trend). Finally, I also present results from a BayesianVAR model with 12 lags and using shrinkage priors. The results turn out to beagain very similar to the baseline VAR (see Figure B.43).

8. Conclusion

Fighting climate change is one of the greatest challenges of our time. Whileit has proved to be very difficult to make progress at the global level, severalnational carbon pricing policies have been put in place. However, still little is

37

known about the effects of these policies on emissions and the economy. Thispaper provides new evidence on the effects of carbon pricing from the largestcarbon market in the world, the EU ETS. I show that tightening the carbon pric-ing regime leads to a persistent fall in emissions and a significant increase inenergy prices. The fall in emissions comes at the cost of temporarily lower eco-nomic activity. The results point to a strong transmission mechanism workingthrough energy prices leading to lower consumption and investment. Impor-tantly, these economic costs are not borne equally across society. Lower-incomehouseholds lower their consumption significantly and are driving the aggregateresponse while richer households are hardly affected. Thus, re-distributing someof the auction revenues to the most affected groups in society may be an effec-tive way to reduce the economic costs of carbon pricing while at the same timestrengthening the public support of the policy.

38

References

Anderson, Soren T., Ioana Marinescu, and Boris Shor. 2019. “Can Pigou at the Polls

Stop Us Melting the Poles?” National Bureau of Economic Research.

Andersson, Julius J. 2019. “Carbon Taxes and CO2 Emissions: Sweden as a Case Study.”

American Economic Journal: Economic Policy, 11(4): 1–30.

Barnichon, Regis and Christian Brownlees. 2019. “Impulse response estimation by

smooth local projections.” Review of Economics and Statistics, 101(3): 522–530.

Baumeister, Christiane and Lutz Kilian. 2017. “A general approach to recovering market

expectations from futures prices with an application to crude oil.”

Bernard, Jean-Thomas, Maral Kichian, and Misbahul Islam. 2018. “Effects of BC’s Car-

bon Tax on GDP.” USAEE Research Paper Series.

Beznoska, Martin, Johanna Cludius, and Viktor Steiner. 2012. “The incidence of the Eu-

ropean Union Emissions Trading System and the role of revenue recycling: Empirical

evidence from combined industry-and household-level data.”

Blanchard, Olivier J. and Roberto Perotti. 2002. “An empirical characterization of the

dynamic effects of changes in government spending and taxes on output.” The Quar-terly Journal of Economics, 117(4): 1329–1368.

Browning, Martin, Angus Deaton, and Margaret Irish. 1985. “A profitable approach to

labor supply and commodity demands over the life-cycle.” Econometrica, 503–543.

Bushnell, James B., Howard Chong, and Erin T. Mansur. 2013. “Profiting from regu-

lation: Evidence from the European carbon market.” American Economic Journal: Eco-nomic Policy, 5(4): 78–106.

Calel, Raphael and Antoine Dechezleprêtre. 2016. “Environmental policy and directed

technological change: evidence from the European carbon market.” Review of Eco-nomics and Statistics, 98(1): 173–191.

Cloyne, James. 2013. “Discretionary tax changes and the macroeconomy: new narrative

evidence from the United Kingdom.” American Economic Review, 103(4): 1507–28.

Cloyne, James and Paolo Surico. 2017. “Household debt and the dynamic effects of in-

come tax changes.” The Review of Economic Studies, 84(1): 45–81.

Cloyne, James, Clodomiro Ferreira, and Paolo Surico. 2020. “Monetary policy when

households have debt: new evidence on the transmission mechanism.” The Review ofEconomic Studies, 87(1): 102–129.

DEHSt, German Emissions Trading Authority. 2019. “German Auctioning of Emission

Allowances: Periodical Report: Annual Report 2018.”

Edelstein, Paul and Lutz Kilian. 2009. “How sensitive are consumer expenditures to

retail energy prices?” Journal of Monetary Economics, 56(6): 766–779.

European Comission. 2020a. “EU Emissions Trading System (EU ETS).” https: // ec.

europa. eu/ clima/ policies/ ets_ en , [Online; accessed 02-Dec-2020].

European Comission. 2020b. “Report on the functioning of the European carbon mar-

39

ket.” https: // ec. europa. eu/ clima/ sites/ clima/ files/ news/ docs/ com_ 2020_

740_ en. pdf , [Online; accessed 02-Dec-2020].

European Comission. 2021. “Fit for 55: delivering the EU’s 2030 Climate Target on the

way to climate neutrality.” https: // eur-lex. europa. eu/ legal-content/ EN/ TXT/

?uri= CELEX: 52021DC0550 , [Online; accessed 30-Aug-2021].

Fan, Ying, Jun-Jun Jia, Xin Wang, and Jin-Hua Xu. 2017. “What policy adjustments in

the EU ETS truly affected the carbon prices?” Energy Policy, 103: 145–164.

Gertler, Mark and Peter Karadi. 2015. “Monetary policy surprises, credit costs, and eco-

nomic activity.” American Economic Journal: Macroeconomics, 7(1): 44–76.

Golosov, Mikhail, John Hassler, Per Krusell, and Aleh Tsyvinski. 2014. “Optimal taxes

on fossil fuel in general equilibrium.” Econometrica, 82(1): 41–88.

Goulder, Lawrence and Marc Hafstead. 2018. Confronting the Climate Challenge.Columbia University Press.

Gürkaynak, Refet S., Brian Sack, and Eric T. Swanson. 2005. “Do actions speak louder

than words? The response of asset prices to monetary policy actions and statements.”

International Journal of Central Banking, 1: 55–93.

Hamilton, James D. 2008. “Oil and the macroeconomy.” The New Palgrave Dictionary ofEconomics, 2.

Hamilton, James D. 2009. “Daily changes in fed funds futures prices.” Journal of Money,credit and Banking, 41(4): 567–582.

Jentsch, Carsten and Kurt G. Lunsford. 2019. “The dynamic effects of personal and cor-

porate income tax changes in the United States: Comment.” American Economic Review,

109(7): 2655–78.

Jordà, Òscar, Moritz Schularick, and Alan M. Taylor. 2015. “Betting the house.” Journalof International Economics, 96: S2–S18.

Kilian, Lutz and Cheolbeom Park. 2009. “The impact of oil price shocks on the US stock

market.” International Economic Review, 50(4): 1267–1287.

Knittel, Christopher R. 2014. “The Political Economy of Gasoline Taxes: Lessons from

the Oil Embargo.” Tax Policy and the Economy, 28(1): 97–131.

Kuttner, Kenneth N. 2001. “Monetary policy surprises and interest rates: Evidence from

the Fed funds futures market.” Journal of Monetary Economics, 47(3): 523–544.

Känzig, Diego R. 2021. “The Macroeconomic Effects of Oil Supply News: Evidence from

OPEC Announcements.” American Economic Review, 111(4): 1092–1125.

Lin, Boqiang and Xuehui Li. 2011. “The effect of carbon tax on per capita CO2 emis-

sions.” Energy policy, 39(9): 5137–5146.

Mansanet-Bataller, Maria and Angel Pardo. 2009. “Impacts of regulatory announce-

ments on CO2 prices.” The Journal of Energy Markets, 2(2): 1–33.

Martin, Ralf, Laure B. De Preux, and Ulrich J. Wagner. 2014. “The impact of a carbon tax

on manufacturing: Evidence from microdata.” Journal of Public Economics, 117: 1–14.

McKibbin, Warwick J., Adele C. Morris, and Peter J. Wilcoxen. 2014. “The economic

40

consequences of delay in US climate policy.”

McKibbin, Warwick J., Adele C. Morris, Augustus Panton, and Peter J. Wilcoxen. 2017.

“Climate change and monetary policy: Dealing with disruption.”

Mertens, Karel and Morten O. Ravn. 2013. “The dynamic effects of personal and corpo-

rate income tax changes in the United States.” American Economic Review, 103(4): 1212–

47.

Metcalf, Gilbert E. 2019. “On the economics of a carbon tax for the United States.” Brook-ings Papers on Economic Activity, 2019(1): 405–484.

Metcalf, Gilbert E. and James H. Stock. 2020a. “The Macroeconomic Impact of Europe’s

Carbon Taxes.” NBER Working Paper.

Metcalf, Gilbert E. and James H. Stock. 2020b. “Measuring the Macroeconomic Impact

of Carbon Taxes.” AEA Papers and Proceedings, 110: 101–06.

Miranda-Agrippino, Silvia and Giovanni Ricco. 2018. “Identification with external in-

struments in structural VARs under partial invertibility.”

Montiel Olea, José Luis and Carolin Pflueger. 2013. “A robust test for weak instru-

ments.” Journal of Business & Economic Statistics, 31(3): 358–369.

Montiel Olea, José Luis and Mikkel Plagborg-Møller. 2020. “Local Projection Inference

is Simpler and More Robust Than You Think.”

Nakamura, Emi and Jón Steinsson. 2018. “High-frequency identification of mone-

tary non-neutrality: The information effect.” The Quarterly Journal of Economics,

133(3): 1283–1330.

Noh, Eul. 2019. “Impulse-response analysis with proxy variables.”

Ohlendorf, Nils, Michael Jakob, Jan Christoph Minx, Carsten Schröder, andJan Christoph Steckel. 2021. “Distributional impacts of carbon pricing: A meta-

analysis.” Environmental and Resource Economics, 78(1): 1–42.

Piazzesi, Monika and Eric T. Swanson. 2008. “Futures prices as risk-adjusted forecasts

of monetary policy.” Journal of Monetary Economics, 55(4): 677–691.

Plagborg-Møller, Mikkel and Christian K. Wolf. 2019. “Local projections and VARs es-

timate the same impulse responses.”

Pretis, Felix. 2019. “Does a carbon tax reduce CO2 emissions? Evidence from British

Columbia.”

Quilis, Enrique M. 2020. “Temporal disaggregation.” https: // www. mathworks. com/

matlabcentral/ fileexchange/ 69800-temporal-disaggregation , [Online; accessed

06-Dec-2020].

Ramey, Valerie A. 2011. “Identifying government spending shocks: It’s all in the timing.”

The Quarterly Journal of Economics, 126(1): 1–50.

Ramey, Valerie A. 2016. “Macroeconomic shocks and their propagation.” In Handbook ofMacroeconomics. Vol. 2, 71–162. Elsevier.

Ramey, Valerie A. and Sarah Zubairy. 2018. “Government spending multipliers in good

times and in bad: evidence from US historical data.” Journal of Political Economy,

41

126(2): 850–901.

Rigobon, Roberto. 2003. “Identification through heteroskedasticity.” Review of Economicsand Statistics, 85(4): 777–792.

Romer, Christina D. and David H. Romer. 2010. “The macroeconomic effects of tax

changes: estimates based on a new measure of fiscal shocks.” American Economic Re-view, 100(3): 763–801.

Sims, Christopher A., James H. Stock, and Mark W. Watson. 1990. “Inference in linear

time series models with some unit roots.” Econometrica, 113–144.

Stefan, Martin and Claudia Wellenreuther. 2020. “London vs. Leipzig: Price discovery

of carbon futures during Phase III of the ETS.” Economics Letters, 188: 108990.

Stock, James H. 2008. “What’s new in Econometrics: Time Series, lecture 7.” NBER Sum-mer Institute Short Course Lectures.

Stock, James H. and Mark W. Watson. 2012. “Disentangling the channels of the 2007-

2009 recession.” Brookings Papers on Economic Activity.

Stock, James H. and Mark W. Watson. 2018. “Identification and estimation of dynamic

causal effects in macroeconomics using external instruments.” The Economic Journal,128(610): 917–948.

Veith, Stefan, Jörg R. Werner, and Jochen Zimmermann. 2009. “Capital market response

to emission rights returns: Evidence from the European power sector.” Energy eco-nomics, 31(4): 605–613.

42

Online Appendix

The economic consequences of putting a price on

carbon

Diego R. Känzig*

London Business School

September, 2021

Contents

A. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3A.1. Details on regulatory events . . . . . . . . . . . . . . . . . . . . . . . 3A.2. Macro data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4A.3. Micro data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

A.3.1. LCFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6A.3.2. LFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9A.3.3. BSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

B. Charts, tables and additional sensitivity checks . . . . . . . . . . . . . . . 9B.1. Diagnostics of the surprise series . . . . . . . . . . . . . . . . . . . . 10B.2. More on aggregate effects . . . . . . . . . . . . . . . . . . . . . . . . 12

B.2.1. Local projection-instrumental variable approach . . . . . . . 12B.2.2. Core versus headline HICP . . . . . . . . . . . . . . . . . . . 14B.2.3. Model with carbon price . . . . . . . . . . . . . . . . . . . . . 15B.2.4. Variance decomposition . . . . . . . . . . . . . . . . . . . . . 16B.2.5. Financial conditions and uncertainty . . . . . . . . . . . . . . 17B.2.6. Aggregate effects for the UK . . . . . . . . . . . . . . . . . . . 17

B.3. More on heterogeneous effects . . . . . . . . . . . . . . . . . . . . . 19B.3.1. Further descriptive statistics . . . . . . . . . . . . . . . . . . . 19B.3.2. Robustness concerning grouping . . . . . . . . . . . . . . . . 21

*Contact: Diego R. Känzig, London Business School, Regent’s Park, London NW1 4SA, UnitedKingdom. E-mail: [email protected]. Web: diegokaenzig.com.

1

B.3.3. Smoothing impulse responses . . . . . . . . . . . . . . . . . . 24B.3.4. Labor versus financial income . . . . . . . . . . . . . . . . . . 25B.3.5. Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27B.3.6. The role of the energy share . . . . . . . . . . . . . . . . . . . 30B.3.7. Direct versus indirect effects . . . . . . . . . . . . . . . . . . . 33B.3.8. External validity . . . . . . . . . . . . . . . . . . . . . . . . . . 40B.3.9. Attitudes towards climate policy . . . . . . . . . . . . . . . . 41

B.4. Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42B.4.1. Selection of events . . . . . . . . . . . . . . . . . . . . . . . . 42B.4.2. Confounding news . . . . . . . . . . . . . . . . . . . . . . . . 47B.4.3. Futures contracts . . . . . . . . . . . . . . . . . . . . . . . . . 52B.4.4. Sample and specification choices . . . . . . . . . . . . . . . . 54

C. Heteroskedasticity-based identification . . . . . . . . . . . . . . . . . . . 61D. A climate DSGE model with heterogeneous agents and sticky prices . . 62

D.1. Overview and results . . . . . . . . . . . . . . . . . . . . . . . . . . . 62D.1.1. Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62D.1.2. Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64D.1.3. Climate block . . . . . . . . . . . . . . . . . . . . . . . . . . . 66D.1.4. Fiscal and monetary policy . . . . . . . . . . . . . . . . . . . 67D.1.5. Aggregation and market clearing . . . . . . . . . . . . . . . . 67D.1.6. Calibration and functional forms . . . . . . . . . . . . . . . . 68D.1.7. Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

D.2. Model derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74D.2.1. Labor market structure . . . . . . . . . . . . . . . . . . . . . . 74D.2.2. Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76D.2.3. Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78D.2.4. Market clearing . . . . . . . . . . . . . . . . . . . . . . . . . . 85D.2.5. Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86D.2.6. Steady state and model solution . . . . . . . . . . . . . . . . . 88

References Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

2

A. Data

A.1. Details on regulatory events

In this Appendix, I provide a detailed list of all the regulatory events used in thepaper. To collect the events, I relied on a number of different sources. After 2010,most of the relevant news can be found on the European Commission Climate Ac-tion news archive: https://ec.europa.eu/clima/news/news_archives_en. Be-fore that, I used information from the official journal of the European Union:https://eur-lex.europa.eu/homepage.html. Finally, the decisions on the NAPsin the first two phases are taken from Mansanet-Bataller and Pardo (2009). TableA.1 lists all the events.

Table A.1: Regulatory update events

Date Event description Type

1 25/05/2005 Italian phase I NAP approved Free alloc.2 20/06/2005 Greek phase I NAP approved Free alloc.3 23/11/2005 Court judgement on proposed amendment to NAP, UK vs Commission Free alloc.4 22/12/2005 Further guidance on allocation plans for the 2008–2012 trading period Cap5 22/02/2006 Final UK Phase I NAP approved Free alloc.6 23/10/2006 Stavros Dimas delivered the signal to tighten the cap of phase II Cap7 13/11/2006 Decision avoiding double counting of emission reductions for projects under the Kyoto Protocol Intl. credits8 29/11/2006 Commission decision on the NAP of several member states Free alloc.9 14/12/2006 Decision determining the respective emission levels of the community and each member state Cap10 16/01/2007 Phase II NAPs of Belgium and the Netherlands approved Free alloc.11 05/02/2007 Slovenia phase II NAP approved Free alloc.12 26/02/2007 Spain phase II NAP approved Free alloc.13 26/03/2007 Phase II NAPs of Poland, France and Czech Republic approved Free alloc.14 02/04/2007 Austrian phase II NAP approved Free alloc.15 16/04/2007 Hungarian phase II NAP approved Free alloc.16 30/04/2007 Court order on German NAP, EnBW AG vs Commission Free alloc.17 04/05/2007 Estonian phase II NAP approved Free alloc.18 15/05/2007 Italian phase II NAP approved Free alloc.19 07/11/2007 Court judgement on German NAP, Germany vs Commission Free alloc.20 08/04/2008 Court order on German NAP, Saint-Gobain Glass GmbH vs Commission Free alloc.21 23/04/2009 Directive 2009/29/EC amending Directive 2003/87/EC to improve and extend the EU ETS Cap22 23/09/2009 Court judgement on NAP, Poland vs Commission Free alloc.23 24/12/2009 Decision determining sectors and subsectors which have a significant risk of carbon leakage Free alloc.24 19/04/2010 Commission accepts Polish NAP for 2008-2012 Free alloc.25 09/07/2010 Commission takes first step toward determining cap on emission allowances for 2013 Cap26 14/07/2010 Member states back Commission proposed rules for auctioning of allowances Auction27 22/10/2010 Cap on emission allowances for 2013 adopted Cap28 12/11/2010 Commission formally adopted the regulation on auctioning Auction29 25/11/2010 Commission presents a proposal to restrict the use of credits from industrial gas projects Intl. credits30 15/12/2010 Climate Change Committee supported the proposal on how to allocate emissions rights Free alloc.31 21/01/2011 Member states voted to support the ban on the use of certain industrial gas credits Intl. credits32 15/03/2011 Commission proposed that 120 million allowances to be auctioned in 2012 Auction33 22/03/2011 Court judgement on NAP, Latvia vs Commission Free alloc.34 29/03/2011 Decision on transitional free allocation of allowances to the power sector Free alloc.35 27/04/2011 Decision 2011/278/EU on transitional Union-wide rules for harmonized free allocation of allowances Free alloc.36 29/04/2011 Commission rejects Estonia’s revised NAP for 2008-2012 Free alloc.37 07/06/2011 Commission adopts ban on the use of industrial gas credits Intl. credits38 13/07/2011 Member states agree to auction 120 million phase III allowances in 2012 Auction39 26/09/2011 Commission sets the rules for allocation of free emissions allowances to airlines Free alloc.40 14/11/2011 Clarification on the use of international credits in the third trading phase Intl. credits41 23/11/2011 Regulation 1210/2011 determining the volume of allowances to be auctioned prior to 2013 Auction42 25/11/2011 Update on preparatory steps for auctioning of phase 3 allowances Auction43 05/12/2011 Commission decision on revised Estonian NAP for 2008-2012 Free alloc.44 29/03/2012 Court judgments on NAPs for Estonia and Poland Free alloc.45 02/05/2012 Commission publishes guidelines for review of GHG inventories in view of setting national limits for 2013-20 Cap46 23/05/2012 Commission clears temporary free allowances for power plants in Cyprus, Estonia and Lithuania Free alloc.47 05/06/2012 Commission publishes guidelines on State aid measures in the context of the post-2012 trading scheme Free alloc.48 06/07/2012 Commission clears temporary free allowances for power plants in Bulgaria, Czech Republic and Romania Free alloc.49 13/07/2012 Commission rules on temporary free allowances for power plants in Poland Free alloc.

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Date Event description Type

50 25/07/2012 Commission proposed to backload certain allowances from 2013-2015 to the end of phase III Auction51 12/11/2012 Commission submits amendment to back-load 900 million allowances to the years 2019-2020 Auction52 14/11/2012 Commission presents options to reform the ETS to address growing supply-demand imbalance Cap53 16/11/2012 Auctions for 2012 aviation allowances put on hold Auction54 30/11/2012 Commission rules on temporary free allowances for power plants in Hungary Free alloc.55 25/01/2013 Update on free allocation of allowances in 2013 Free alloc.56 28/02/2013 Free allocation of 2013 aviation allowances postponed Free alloc.57 25/03/2013 Auctions of aviation allowances not to resume before June Auction58 16/04/2013 The European Parliament voted against the Commission’s back-loading proposal Auction59 05/06/2013 Commission submits proposal for international credit entitlements for 2013 to 2020 Intl. credits60 03/07/2013 The European Parliament voted for the carbon market back-loading proposal Auction61 10/07/2013 Member states approve addition of sectors to the carbon leakage list for 2014 Free alloc.62 30/07/2013 Update on industrial free allocation for phase III Free alloc.63 05/09/2013 Commission finalized decision on industrial free allocation for phase three Free alloc.64 26/09/2013 Update on number of aviation allowances to be auctioned in 2012 Auction65 08/11/2013 Member states endorsed negotiations on the back-loading proposal Auction66 21/11/2013 Commission submitted non-paper on back-loading to the EU Climate Change Committee Auction67 10/12/2013 European Parliament voted for the back-loading proposal Auction68 11/12/2013 Climate Change Committee makes progress on implementation of the back-loading propsal Auction69 18/12/2013 Commission gives green light for a first set of member states to allocate allowances for calendar year 2013 Free alloc.70 08/01/2014 Climate Change Committee agrees back-loading Auction71 22/01/2014 Commission proposed to establish a market stability reserve for phase V Cap72 26/02/2014 Commission gives green light for free allocation by all member states Free alloc.73 27/02/2014 Back-loading: 2014 auction volume reduced by 400 million allowances Auction74 13/03/2014 Commission approves first batch of international credit entitlement tables Intl. credits75 28/03/2014 Commission approves second batch of international credit entitlement tables Intl. credits76 04/04/2014 Update on approval of international credit entitlement tables Intl. credits77 11/04/2014 Commission approves four more international credit entitlement tables Intl. credits78 23/04/2014 Commission approves final international credit entitlement tables Intl. credits79 02/05/2014 Commission published the number of international credits exchanged Intl. credits80 05/05/2014 Commission submits proposed carbon leakage list for 2015-2019 Free alloc.81 04/06/2014 Auctioning of aviation allowances to restart in September Auction82 04/07/2014 Commission published the first update on the allocation of allowances from the New Entrants’ Reserve Free alloc.83 09/07/2014 Climate Change Committee agrees proposed carbon leakage list for the period 2015-2019 Free alloc.84 27/10/2014 Commission adopts the carbon leakage list for the period 2015-2019 Free alloc.85 04/11/2014 Updated information on exchange and international credit use Intl. credits86 04/05/2015 Updated information on exchange and international credit use Intl. credits87 15/07/2015 Proposal to revise the EU emissions trading system for the period after 2020 Cap88 23/07/2015 Commission publishes status update for New Entrants’ Reserve and allocation reductions Free alloc.89 04/11/2015 Updated information on exchange and international credit use Intl. credits90 15/01/2016 Commission publishes status update for New Entrants’ Reserve Free alloc.91 28/04/2016 Court judgment on free allocation in the EU ETS for the period 2013-2020 Free alloc.92 02/05/2016 Updated information on exchange and international credit use Intl. credits93 23/06/2016 Following court judgement, commission to modify cross-sectoral correction factor for 2018-2020 Free alloc.94 15/07/2016 Commission published a status update on the allocation of allowances from the New Entrants’ Reserve 2013-2020 Free alloc.95 08/09/2016 Court judgment on free allocation in the EU ETS for the period 2013-2020 Free alloc.96 04/11/2016 Updated information on exchange and international credit use Intl. credits97 16/01/2017 Commission publishes status update for New Entrants’ Reserve Free alloc.98 24/01/2017 Commission adopts Decision to implement Court ruling on the cross-sectoral correction factor Free alloc.99 15/02/2017 European Parliament voted in support of the revision of the ETS Directive for the period after 2021 Cap100 27/04/2017 Climate Change Committee approves technical changes to auction rules Auction101 02/05/2017 Updated information on exchange and international credit use Intl. credits102 12/05/2017 Commission publishes first surplus indicator for ETS Market Stability Reserve Auction103 17/07/2017 Commission publishes status update for New Entrants’ Reserve Free alloc.104 26/07/2017 Court judgment again confirms benchmarks for free allocation of ETS allowances for 2013-2020 Free alloc.105 06/11/2017 Updated information on exchange and international credit use Intl. credits106 15/01/2018 Commission publishes status update for New Entrants’ Reserve Free alloc.107 04/05/2018 Updated information on exchange and international credit use Intl. credits108 08/05/2018 Commission Notice on the preliminary carbon leakage list for phase IV (2021-2030) Free alloc.109 15/05/2018 ETS Market Stability Reserve will start by reducing auction volume by almost 265 million allowances Auction110 16/07/2018 Commission publishes status update for New Entrants’ Reserve Free alloc.111 30/10/2018 Commission adopts amendment to ETS auctioning regulation Auction112 06/11/2018 Updated information on exchange and international credit use Intl. credits113 05/12/2018 Poland’s 2019 auctions to include some allowances not used for power sector modernization Auction

A.2. Macro data

In this Appendix, I provide details on the macroeconomic data used in the paper,including information on the data source and coverage.

4

Table A.2: Data description, sources, and coverage

Variable Description Source Sample

Instrument

LEXC.01 (PS) EUA futures front contract (settlement price) Datastream 22/04/2005-31/12/2018

Baseline variables

EKESCPENF HICP energy (EA-19) Datastream 1999M1-2018M12GHGTOTAL Total GHG emissions excluding LULUCF and includ-

ing international aviation (EU)Eurostat/own cal-culations

1999M1-2018M12

EKCPHARMF HICP all items (EA-19) Datastream 1999M1-2018M12EKIPTOT.G Industrial production excl. construction (EA-19) Datastream 1999M1-2018M12EMINTER3 3-month Euribor Datastream 1999M1-2018M12EKESUNEMO Unemployment rate (EA-19) Datastream 1999M1-2018M12DJSTO50 Euro STOXX 50 Datastream 1999M1-2018M12RBXMBIS Broad REER (EA) FRED 1999M1-2018M12

Additional variables

Other carbon futures LEXC.0h (PS), for h in (2, 3, 4, 5) Datastream 22/04/2005-31/12/2018

Sectoral stock prices Market [DJSTOXX], Utilities [S1ESU1E] Datastream 22/04/2005-31/12/2018

BAMLHE00EHYIOAS ICE BofA euro high yield index option-adj. spread FRED 1999M1-2018M12VSTOXX Euro STOXX 50 volatility stoxx.com 1999M1-2018M12EKGDP...D Real GDP (EA-19) Datastream 1999M1-2018M12EKESENMZD Final consumption expenditure (EA-19) Datastream 1999M1-2018M12EKGFCF..D Gross fixed capital formation (EA-19) Datastream 1999M1-2018M12EKNX Net exports [EKEXNGS.D-EKIMNGS.D] as a share of

GDP [EKGDP...D] (EA-19)Datastream/owncalculations

1999M1-2018M12

CCPATENTS Share of climate change mitigation technologies(CCMT) patents filed at EPO

Google Patents Pub-lic Data/own calcu-lations

2005Q1-2018Q4

The transformed series used in the baseline VAR are depicted in Figure A.1.

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Figure A.1: Transformed data series

A.3. Micro data

In this Appendix, I provide detailed information on the micro data used in Sec-tion 6 of the paper. I use data from a selection of different surveys, which arediscussed in detail below.

A.3.1. LCFS

The living costs and food survey (LCFS) data can be obtained from the UK DataService. I use the waves from 1999-2001 of the Family Expenditure Survey, the2001-2007 waves from the Expenditure and Food Survey and the 2008-2019 wavesfrom the LCFS, which superseded the previous two surveys. Note that withinthis sample, the reporting frequency changed two times first from financial yearto calendar year and then back again to the financial year format. The wavesare adjusted to consistently reflect the calendar year prior to creating the pooledcross-section. Most variables of interest are available in the derived householddatasets. The age at which full-time education was completed, as well as currentwages, is aggregated from the personal derived datasets.

6

As the main measure of expenditure, I use total expenditure excluding hous-ing (p550tp-p536tp). For current income, I use current total disposable income,calculated by subtracting income taxes and NI contributions from the gross in-come (p352p-p392p-p388p-p029hp). I group the households by their normal dis-posable income (p389p). For earnings, I use wages net of taxes (aggregate p004pto the household level, subtract current taxes and add back taxes on financial in-come p068h). For financial income, I use p324p, which includes interest income,dividends and rents. For age, I use the age of the household reference person,p396p. Education is proxied by the highest age a person in the household hascompleted a full-time education (a010 aggregated to the household level). Thehousing tenure status is recorded in variable a121.

For energy expenditure, I use expenditure on fuel, light and power (p537t).Constructing measures of non-durable, services and durable expenditure is nottrivial in the LCFS data, as the broader available expenditure categories do not al-low a clean split, e.g. personal goods and services (p544t) is a mix of non-durablegoods and services while household goods (p542t) includes both non-durableand durable goods. To construct clean measures of non-durables, services anddurables expenditure, I split these broader subcategories into non-durable, ser-vices and durable parts by grouping the items in a particular subcategory accord-ingly, following closely the COICOP guidelines. A further challenge in doing sois that the code names for disaggregated expenditure items changed when theFES became the EFS in 2001. In Table A.3, I detail how the non-durable, servicesand durable expenditure measures are constructed. At the item level, I provideboth, the relevant codes in the FES and the EFS/LCFS. Note that semi-durablesare subsumed under non-durables, and services do not include housing.

Table A.3: Expenditure classification in LCFS

Category Subcategories Items

Non-durables Fuel, light power (p537t)Food, alcoholic drinks, tobacco(p538t, p539t, p540t)Clothing and footwear (p541t)Non-durable household goods(subset of p542t)

LCFS codes: c52111t, c52112t, c53311t, c55214t, c56111t,c56112t, c56121t, c56123t, c93114t, c93313t, c93411t, c95311t,c95411t, cc1311tFES codes: d070104t, d070105t, d070211t, d070209t, d070401t,d070402t, d070302t, d070601t, d120304t, d070501t

Non-durable personal goods(subset of p544t)

LCFS codes: c61112t, c61211t, c61311t, c61313t, cc1312t,cc1313t, cc1314t, cc1315t, cc1316t, cc1317t, cc3211t, cc3222t,cc3223t, cc3224tFES codes: d090402t, d090102t, d090501t, d090101t, d090103t,d090104t, d090105t, d090301t, d090202t, d090302t, d090303t

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Category Subcategories Items

Non-durable motoring expenditure(subset of p545t)

LCFS codes: c72114t, c72211t, c72212t, c72213tFES codes: d100405t, d100301t, d100302t, d100303t

Non-durable leisure goods(subset of p547t)

LCFS codes: c91126t, c91411t, c91412t, c91413t, c91414t,c93111t, c93113t, c93311t, c95111t, c95211t, c95212tFES codes: d120114t, d120108t, d120110t, d120109t, d120401t,d120113t, d070703t, d120303t, d120301t, d120302t

Miscellaneous non-durable goods(subset of p549t)

LCFS codes: ck5511c, cc3221tFES codes: d070801t, d140601c, d090701t

Services Household services (p543t)Fares and other travel costs (p546t)Leisure services (p548t)Service part of household goods(subset of p542t)

LCFS codes: c53312t, c53313t, c53314t, c93511t, cc5213tFES codes: d070212t, d070213t

Personal services(subset of p544t)

LCFS codes: c61111t, c61312t, c62111t, c62112t, c62113t,c62114t, c62211t, c62212t, c62311t, c62321t, c62322t, c62331t,c63111t, cc1111tFES codes: d090401t, d090502t, d090403t, d090404t, d090601t

Service part of motoring expendi-ture (subset of p545t)

LCFS codes: b187-b179, b188, b249, b250, b252, c72313t,c72314t, c72411t, c72412t, c72413t, ck3112t, c72311c, c72312c,cc5411cFES codes: b187-b179, b188, b249, b250, b252, d100403t,d100406t, d100407t, d100404t, d100408t, d100201c, d100204c,d100401c

Leisure services(subset of p547t)

LCFS codes: c91511t, c93112t, c94238t, c94239t, c94246tFES codes: d120111t, d120112t

Miscellaneous services(subset of p549t)

LCFS codes: b237, b238, ck5315c, ck5213t, ck5214tFES codes: b237, b238, d140402, d140406c

Durables Durable household goods(subset of p542t)

LCFS codes: b270, b271, c51111c, c51211c, c51212t, c51113t,c51114t, c53111t, c53121t, c53122t, c53131t, c53132t, c53133t,c53141t, c53151t, c53161t, c53171t, c53211t, c54111t, c54121t,c54131t, c54132t, c55111t, c55112t, c55213t, c56122t, c93212t,c93312t, c93412t, cc1211tFES codes: b270, b271, d070101c, d070102c, d070103t,d070304t, d070704t, d070203t, d070202t, d070204t, d070207t,d070208t, d070201t, d070206t, d070303t, d070301t, d070205t,d070701t, d070305t, d070306t, d070702t, d070602t

Durable personal goods(subset of p544t)

LCFS codes: cc3111tFES codes: d090201t

Durable motoring expenditure(subset of p544t)

LCFS codes: b244, b2441, b245, b2451, b247, c31315t, c71112t,c71122t, c71212t, c92114t, c92116t, c71111c, c71121c, c71211c,c92113c, c92115c, c72111t, c72112t, c72113t, c91112tFES codes: b244, b245, b247, d100105t, d100106t, d100107t,d100101c, d100102c, d100104c, d100203t, d100202t, d100205t

Durable leisure goods(subset of p547t)

LCFS codes: c91124t, c82111t, c82112t, c82113t, c91111t,c91113t, c91121t, c91122t, c91123t, c91125t, c91211t, c91311t,c92211t, c92221t, c93211tFES codes: d120104t, d080202t, d080205t, d080207t, d120105t,d120101t, d120102t, d120103t, d120115t, d120402t, d120106t,d120107t, d120201t

Regarding the sample, I apply the following restrictions. I drop householdsthat have a household reference person younger than 18 or older than 90 years.

8

Furthermore, I drop households with a negative normal disposable income. Toaccount for some (unrealistically) high or low values of consumption, for eachquarter and income group, I drop the top and bottom 1% of observations for totalexpenditure.

A.3.2. LFS

To get information on the sector of employment, I use data from the UK LabourForce Survey (LFS). The LFS studies the employment circumstances of the UKpopulation. It is the largest household study in the UK and provides the officialmeasures of employment and unemployment. Apart from detailed informationon employment, it also contains a wide range of related topics such as occupation,training, hours of work and personal characteristics of household members aged16 years and over. The data can be obtained from the UK Data Service. I usethe quarterly waves from 1999-2018 to construct a pooled cross-section. For theemployment sector, I use the variable indsect, which describes the industry sectorin the main job based on the SIC 2003 classification. To proxy income, I use thenet pay from the main and second job (netwk and netwk2).

A.3.3. BSA

To proxy public attitudes towards climate policy, I use data from the British socialattitudes (BSA) survey. The data can also be obtained from the UK Data Service. Iuse the waves from 1999-2018 to construct a pooled cross-section. To construct theincome groups, I use the income quartiles that are provided from 2010 onwards(hhincq). For the years before, I use the household income variable (hhincome)to construct the quartiles. The survey contains many questions on the attitudestowards climate change, the environment and climate/environmental policy, butunfortunately most variables are not part of the main set of questions that areasked in every year. One exception concerns a question about taxes for car owners(cartaxhi), in particular it asks whether you agree with the following statement:“For the sake of the environment, car users should pay higher taxes”, which wasfielded for all years up to 2017. Thus, I use the proportion of households agreeingwith this statement as a proxy for the public attitude towards climate policy.

B. Charts, tables and additional sensitivity checks

In this Appendix, I present additional tables and figures, and sensitivity checksthat are not featured in the main body of the paper.

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B.1. Diagnostics of the surprise series

As discussed in the paper, I perform a number of additional validity checks on thesurprise series. In particular, I investigate the autocorrelation and forecastabilityof the surprise series as well as the relation to other shocks from the literature.

Figure B.1: The autocorrelation function of the carbon policy surprise series

Figure B.1 depicts the autocorrelation function. We can see that there is littleevidence that the series is serially correlated. I also perform a number of Grangercausality tests. Table B.1 shows that the series is not forecastable by past macroe-conomic or financial variables. Finally, I look how the series correlates with othershock series from the literature and find that it is not correlated with other struc-tural shock measures, including oil, uncertainty, financial, fiscal and monetarypolicy shocks (see Table B.2).

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Table B.1: Granger causality tests

Variable p-value

Instrument 0.9066EUA price 0.7575HICP energy 0.7551GHG emissions 0.7993HICP 0.8125Industrial production 0.7540Policy rate 0.9414Unemployment rate 0.9310Stock prices 0.9718REER 0.9075Joint 0.9997

Notes: The table shows the p-values of a series of Granger causality tests of the carbonpolicy surprise series using a selection of macroeconomic and financial variables.

Table B.2: Correlation with other shock measures

Shock Source ρ p-value n Sample

Monthly measuresGlobal oil marketOil supply Kilian (2008) (extended) -0.05 0.61 104 2005M05-2013M12

Kilian (2009) (updated) -0.02 0.76 164 2005M05-2018M12Caldara, Cavallo, and Iacoviello (2019) -0.05 0.57 128 2005M05-2015M12Baumeister and Hamilton (2019) -0.11 0.17 164 2005M05-2018M12Känzig (2021) (updated) 0.02 0.83 164 2005M05-2018M12

Global demand Kilian (2009) (updated) 0.01 0.93 164 2005M05-2018M12Baumeister and Hamilton (2019) -0.03 0.69 164 2005M05-2018M12

Oil-specific demand Kilian (2009) (updated) 0.05 0.55 164 2005M05-2018M12Consumption demand Baumeister and Hamilton (2019) 0.05 0.51 164 2005M05-2018M12Inventory demand Baumeister and Hamilton (2019) -0.03 0.68 164 2005M05-2018M12

Monetary policyMonetary policy shock Jarocinski and Karadi (2020) 0.02 0.80 140 2005M05-2016M12Central bank info Jarocinski and Karadi (2020) 0.03 0.75 140 2005M05-2016M12

Financial & uncertaintyFinancial conditions BBB spread residual 0.06 0.43 164 2005M05-2018M12Financial uncertainty VIX residual (Bloom, 2009) 0.10 0.22 164 2005M05-2018M12

VSTOXX residual 0.05 0.50 164 2005M05-2018M12Policy uncertainty Global EPU (Baker, Bloom, and Davis, 2016) 0.03 0.71 164 2005M05-2018M12

Quarterly measuresFiscal policy Euro area (Alloza, Burriel, and Pérez, 2019) 0.12 0.44 43 2005Q2-2015Q4

Germany 0.22 0.15 43 2005Q2-2015Q4France -0.06 0.69 43 2005Q2-2015Q4Italy 0.28 0.07 43 2005Q2-2015Q4Spain 0.10 0.52 43 2005Q2-2015Q4

Notes: The table shows the correlation of the carbon policy surprise series with a widerange of different shock measures from the literature, including global oil market shocks,monetary policy, financial and uncertainty shocks. ρ is the Pearson correlation coefficient,the p-value corresponds to the test whether the correlation is different from zero and n isthe sample size.

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B.2. More on aggregate effects

In this Appendix, I present some additional results pertaining to the analysis inSection 5 in the paper.

B.2.1. Local projection-instrumental variable approach

As discussed in the main text, I rely on VAR techniques for estimation becausethe sample is relatively short and VARs provide a parsimonious characterizationof the data. However, as a robustness check, I have also tried to estimate the im-pulse responses using a local projections instrumental variable (LP-IV) approachà la Jordà, Schularick, and Taylor (2015) and Ramey and Zubairy (2018). To fixideas, the dynamic causal effects, ψi

h, can be estimated from the following set ofregressions:

yi,t+h − yi,t−1 = βi0 + ψi

h∆y1,t + βi′hxt−1 + ξi,t,h, (1)

using zt as an instrument for ∆y1,t. Here, yi,t+h is the outcome variable of interest,∆y1,t is the endogenous regressor, xt−1 is a vector of controls, ξi,t,h is a potentiallyserially correlated error term, and h is the impulse response horizon. For infer-ence, I follow again the lag-augmentation approach proposed by Montiel Oleaand Plagborg-Møller (2020).

As the impacts of carbon policy are potentially very persistent, we want tolook at the dynamic causal effects relatively far out. Given the short sample, thisis challenging in the LP-IV framework, which does not use the parametric VARrestriction but estimates the effect by a distinct IV regression at each horizon h.Consequently, the number of observations available for estimation decreases withthe impulse horizon. Against this background, I restrict the impulse horizon inthe LP-IV regressions to 20 months.

Figure B.2 compares the responses obtained from the LP-IV approach to theones from the internal instrument VAR. Recall that both approaches rely on thesame invertibility-robust identifying restrictions but use different estimation tech-niques. We can see that the two approaches produce consistent results, especiallyat horizons up to one year.1 At longer horizons the differences tend to be larger,however, the responses are also much less precisely estimated.

1Note that this is despite the fact that we only control for 6 lags in both models.

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Figure B.2: Robustness with respect to estimation strategy

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid dark and red lines are the point estimates forthe internal instrument VAR and the LP-IV, respectively, and the shaded areas / dashedlines are 68 and 90 percent confidence bands.

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B.2.2. Core versus headline HICP

In the paper, we have documented a significant and persistent increase in head-line HICP. An important question that has also relevant implications for the con-duct of monetary policy is how the shock transmits to core consumer prices. Tothis end, I re-estimate the model substituting headline for core HICP. Figure B.3presents the response for core HICP together with the HICP headline and energycomponents from the baseline model. We can see that the response of core con-sumer prices is more muted and much less precisely estimated. Importantly, theresponse also turns out to be much less persistent, which may reflect the fact thatthe fall in economic activity exerts downward pressure on prices other than en-ergy, such as services. Reassuringly, all other responses from the model with coreHICP are very similar to the baseline case.

Figure B.3: Robustness with respect to estimation strategy

Notes: Impulse responses of the headline, energy and core HICP to a carbon policy shock.The headline and energy indices are from the baseline model; the core response is fromthe model featuring core instead of headline HICP. The solid line is the point estimateand the dark and light shaded areas are 68 and 90 percent confidence bands, respectively.

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B.2.3. Model with carbon price

Recall, the baseline model does not include the carbon price as information onprices are only available from 2005 when the carbon market was established. Asa robustness check, I estimate a model including the carbon price in lieu of GHGemissions on the shorter sample starting from 2005. The results are depicted inFigure B.4. We can see that the shock leads to a significant increase in the car-bon price, in line with the interpretation of a shock tightening the carbon pricingregime. Interestingly, however, the carbon price response turns out to be lesspersistent than the energy price response. We can also back out the elasticity ofenergy to carbon prices, which turns out to be around 20 percent at the peak.

Figure B.4: Model including carbon spot price

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

15

B.2.4. Variance decomposition

To better understand how carbon policy shocks have contributed to variationsin macroeconomic and financial variables, I perform a variance decompositionin addition to the historical decomposition presented in the paper. I do so bothunder the invertibility assumption maintained in the external instrument VAR aswell as under weaker assumptions in the context of a general SVMA model, asproposed by Plagborg-Møller and Wolf (2020). In particular, I perform a standardforecast error variance decomposition in the SVAR and compute forecast varianceratios for the SVMA. The forecast variance ratio for variable i at horizon h is givenby

FVRi,h = 1− Var(yi,t+h|yτ−∞<τ≤t, ε1,τt<τ<∞)

Var(yi,t+h|yτ−∞<τ≤t), (2)

and measures the reduction in the econometrician’s forecast variance that wouldarise from being told the entire path of future realizations of the shock of interest.Plagborg-Møller and Wolf (2020) show that this statistic is interval-identified un-der the assumption that a valid instrument is available. Under the assumption ofrecoverablity, the ratio is point-identified and given by the upper bound.

The results are shown in Table B.3. We can see that carbon policy shocks havecontributed meaningfully to historical variations in the variables of interest. Un-der the invertibility assumption (Panel A), they account for about 40 percent ofthe variations in energy prices and around 10 percent of the short-run variationsin emissions, which goes up to almost 40 percent at the 5 year horizon. Turningto the macroeconomic variables, we can see that they explain a substantial partof variations in the HICP, especially at shorter horizons, and a significant fractionof the variations in industrial production and the unemployment rate at longerhorizons. The contributions to variations in the policy rate, stock prices and theREER are lower but still non-negligible.

The forecast variance ratios in Panel B, which dispense from the assumptionof invertibility, paint a slightly more nuanced picture. In many cases, the pointestimates from the external instrument VAR lie within the estimated intervals.The largest differences arise for the contributions to stock prices and the REERwhich are estimated to be significantly lower when allowing for non-invertibility.However, overall the two approaches produce comparable results.

16

Table B.3: Variance decomposition

h HICP energy Emissions HICP IP Policy rate Unemp. rate Stock prices REER

Panel A: Forecast variance decomposition (assuming invertibility)6 0.42 0.12 0.49 0.02 0.00 0.07 0.13 0.00

[0.20, 0.83] [0.02, 0.41] [0.26, 0.87] [0.00, 0.08] [0.00, 0.01] [0.01, 0.56] [0.03, 0.65] [0.00, 0.01]12 0.34 0.25 0.35 0.15 0.03 0.23 0.15 0.00

[0.14, 0.73] [0.07, 0.70] [0.14, 0.69] [0.04, 0.48] [0.01, 0.18] [0.06, 0.84] [0.04, 0.66] [0.00, 0.01]24 0.36 0.32 0.25 0.27 0.13 0.37 0.11 0.09

[0.15, 0.70] [0.11, 0.74] [0.08, 0.56] [0.09, 0.65] [0.03, 0.53] [0.12, 0.90] [0.03, 0.48] [0.03, 0.27]60 0.38 0.39 0.17 0.22 0.11 0.38 0.12 0.25

[0.18, 0.71] [0.16, 0.72] [0.05, 0.45] [0.08, 0.55] [0.03, 0.41] [0.13, 0.82] [0.03, 0.45] [0.08, 0.56]

Panel B: Forecast variance ratio (robust to non-invertibility)6 0.04, 0.31 0.02, 0.18 0.07, 0.49 0.02, 0.14 0.00, 0.02 0.05, 0.35 0.00, 0.03 0.00, 0.00

[0.02, 0.54] [0.01, 0.41] [0.04, 0.74] [0.01, 0.34] [0.00, 0.05] [0.02, 0.59] [0.00, 0.08] [0.00, 0.02]12 0.05, 0.33 0.03, 0.18 0.07, 0.50 0.02, 0.16 0.00, 0.02 0.05, 0.36 0.01, 0.04 0.00, 0.01

[0.03, 0.53] [0.01, 0.36] [0.04, 0.73] [0.01, 0.33] [0.00, 0.05] [0.03, 0.60] [0.00, 0.08] [0.00, 0.02]24 0.05, 0.32 0.03, 0.19 0.07, 0.50 0.02, 0.18 0.01, 0.08 0.08, 0.55 0.01, 0.04 0.00, 0.01

[0.02, 0.52] [0.01, 0.36] [0.04, 0.72] [0.01, 0.35] [0.01, 0.19] [0.04, 0.78] [0.00, 0.09] [0.00, 0.02]60 0.05, 0.32 0.03, 0.19 0.07, 0.50 0.02, 0.18 0.01, 0.08 0.09, 0.55 0.01, 0.04 0.00, 0.01

[0.02, 0.52] [0.01, 0.35] [0.04, 0.72] [0.01, 0.35] [0.00, 0.18] [0.04, 0.78] [0.00, 0.09] [0.00, 0.02]

Notes: The table shows variance decomposition at horizons ranging from 6 months to5 years. Panel A includes the forecast error variance decomposition from the externalinstrument VAR with the point estimates and the 90% confidence interval in brackets.Panel B shows the identified set for the forecast variance ratio together with the 90%confidence interval in brackets.

B.2.5. Financial conditions and uncertainty

To better understand how the shock transmits to the economy, I have also lookedat the responses of indicators for financing conditions and financial uncertainty,see Figure B.5. However, as can be seen from the responses these variables do notappear to play a dominant role in the transmission of the carbon policy shock.

Figure B.5: Financial and uncertainty indicatorsNotes: Impulse responses of financial conditions, as proxied by the BBB bond spread,and the VSTOXX index as a measure of financial uncertainty.

B.2.6. Aggregate effects for the UK

Because of data availability, the household-level analysis is carried out for theUK. For better comparison, I have verified that the aggregate effects on the UK,

17

as measured by real GDP, consumption and investment, are comparable to theEU level responses, see Figure B.6.

Figure B.6: Effect on UK GDP and components

Notes: Impulse responses of UK real GDP, consumption, investment and net exportsexpressed as a share of GDP.

Finally, I have also estimated the baseline model using UK data for macroeco-nomic block. The results are depicted in Figure B.7. We can see that the resultsare comparable to the model with the EU block, even though the first stage turnsout to be weaker and the responses are less precisely estimated.

18

Figure B.7: Model with block for UK economy

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively. I keep the carbonblock of the model at the EU level and replace the macro block with the correspondingvariables for the UK.

B.3. More on heterogeneous effects

In this Appendix, I present some additional results pertaining to Section 6 on theheterogeneous effects of carbon pricing in the paper.

B.3.1. Further descriptive statistics

Figure B.8 compares the empirical distribution of age and total expenditure forthe three income groups. We can see that the groups are comparable in terms oftheir age distribution. As expected, higher income groups tend to have higher

19

expenditure but there is also more within group variation.

Figure B.8: Empirical distribution of age and total expenditure in the LCFS

Notes: The figure shows the empirical probability distribution of age and total expendi-ture (excl. housing) for all three income groups. The distributions are estimated using anEpanechnikov kernel.

Figure B.9 depicts the evolution of different households characteristics, in-cluding age, education and housing tenure, over time. We can see that there aresome trends in these variables, however, they are rather slow-moving and thusunlikely to confound potential heterogenities in the household responses to car-bon policy shocks, which exploit variation at a much higher frequency.

Figure B.9: Evolution of household characteristics by income group

Notes: The figure shows the evolution of age, education, and housing tenure status overtime by income group.

20

B.3.2. Robustness concerning grouping

To mitigate concerns about endogenous changes in the grouping variable, I lookat the responses of current and normal disposable income in Figure B.10. Wecan see that both variables are rather slow-moving. Current income starts to fallsignificantly after about a year. In contrast, the response of normal disposableincome is insignificant, at least at the 10 percent level, supporting its validity as agrouping variable.

Figure B.10: Responses of current and normal income

Notes: Impulse responses of current disposable income and normal disposable income.

As a robustness check, I use a selection of other proxies for the income level,including earnings, expenditure, and an estimate for permanent income obtainedfrom a Mincerian-type regression. For the latter, I use age, education, ethnicity,sex, martial status, occupation, the source of the main household income, as wellas interactions between age and education, and between age and sex as predic-tors, as in Alves et al. (2020). From Figures B.11-B.13, we can see that the resultsturn out to be robust.

21

Figure B.11: Expenditure and income responses by earnings groups

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income by earnings (incl. benefits) groups (bottom 25 percent, middle50 percent, top 25 percent).

22

Figure B.12: Expenditure and income responses by expenditure groups

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income by groups of total expenditure as a proxy for permanent in-come (bottom 25 percent, middle 50 percent, top 25 percent).

23

Figure B.13: Expenditure and income responses by permanent income

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income by permanent income, estimated using a Mincerian-type re-gression using age, education, ethnicity, sex, martial status, occupation, the source of themain household income, as well as interactions between age and education, and betweenage and sex (bottom 25 percent, middle 50 percent, top 25 percent).

B.3.3. Smoothing impulse responses

In the LCFS, households interviewed at time t are typically asked to report ex-penditure over the previous three months (with the exception of non-durableconsumption which refers to the previous two weeks). To eliminate some of thenoise inherent in survey data, I smooth the expenditure and income measureswith a backward-looking (current and previous three quarters) moving average,as in Cloyne, Ferreira, and Surico (2020). However, as shown in Figure B.14, theresults are very similar when using the raw series instead, even though the re-sponses become more jagged and imprecise, or by using smooth local projectionsas proposed by Barnichon and Brownlees (2019).

24

Figure B.14: Sensitivity with respect to smoothing of responses

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income by income group, computed using simple backward-lookingmoving average (baseline), smooth local projections (red dotted line), and unsmoothed(blue dashed line).

B.3.4. Labor versus financial income

To better understand how the current income of households in different incomegroups responds, I study the responses of labor earnings and financial income.We can see that the earnings of low-income households fall more promptly andsignificantly than for higher-income households. On the other hand, the financialincome of low- and middle-income households barely shows a response, reflect-ing the fact that these households own very little financial assets. In contrast,high-income households experience a significant fall in their financial incomein the short run, which however subsequently reverts (consistent with the stockmarket response).

25

Figure B.15: Responses of earnings and financial income

Notes: Impulse responses of labor earnings (wages from main occupation) and finan-cial income (interest, dividend, rents) by income group (bottom 25 percent, middle 50percent, top 25 percent).

26

B.3.5. Selection

To mitigate concerns about selection, I use a number of different grouping vari-ables, including age, education and housing tenure. From Figures B.16-B.18, wecan see that none of these alternative grouping variables can account for the pat-terns uncovered for income, suggesting that we are not spuriously picking updifferences in other household characteristics. Similarly, the uncovered hetero-geneity can also not be accounted for by occupation, sex and region. These resultsare available from the author upon request.

Figure B.16: Household expenditure and income responses by age groups

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income for young (bottom 33 percent), middle-aged and older house-holds (top 33 percent), based on the age of the household head.

27

Figure B.17: Household expenditure and income responses by education status

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income for less educated, normally educated and well educatedhouseholds. Education status is proxied by the highest age a household member hascompleted full-time education and the three groups are below 16 years, between 17 and18 years (compulsory education), and 19 years or above (post-compulsory).

28

Figure B.18: Household expenditure and income responses by housing tenure

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income for social renters, mortgagors and outright owners.

29

B.3.6. The role of the energy share

To further analyze the role of the energy share, I look at the responses of energyexpenditure – in absolute terms and as a share of total expenditure.2 From FigureB.19, we can see that energy expenditure falls slightly on impact but then tends toincrease. However, the response is barely significant. This is also reflected in theresponse of the energy share, which also has a tendency to increase, even thoughthe response is insignificant at the 10 percent level. Figure B.20 further presentsthe energy expenditure responses by income group. We can see that energy ex-penditure turns out to be pretty inelastic, especially for low-income households.Higher-income households display a somewhat higher elasticity, however, theirenergy share does not appear to change significantly after the shock.

Figure B.19: Responses of energy expenditure and the energy share

Notes: Impulse responses of energy expenditure (expenditure on fuel, light and power)and the budget share of energy (expenditure on fuel, light and power as a share of totalexpenditure).

2To compute real energy expenditure, I deflate nominal energy expenditure by the energycomponent of the (harmonized) consumer price index.

30

Figure B.20: Energy expenditure and energy share by income group

Notes: Impulse responses of energy expenditure and the budget share of energy by in-come group (bottom 25 percent, middle 50 percent, top 25 percent).

A key difference between high- and low-income households concerns theirenergy share. However, as we have argued, heterogeneity in the energy sharealone cannot account for the heterogeneous expenditure responses. To make therole of the energy share in the transmission of carbon pricing more explicit, I al-ternatively group households by their energy share, i.e. households with a highenergy share, households with a normal energy share, and households with alow energy share. Table B.4 provides descriptive statistics on income, expendi-ture and other characteristics by the households’ energy share. Note that theheterogeneity in the energy share is now (by construction) much starker: close to16 percent in the high-share group against only around 2 percent for low-sharehouseholds. Importantly, the high-, middle- and low-energy share groups turnout to be comparable to the low-, middle- and high-income groups along manyother dimensions. In particular, the levels of expenditure and income turn out

31

to be decreasing in the energy share. The largest differences are that high-energyshare households tend to be older and more likely to be homeowners than house-holds in the low-income group.

Table B.4: Descriptive statistics on households in the LCFS

Overall By energy share

High-share Middle-share Low-share

Income and expenditureNormal disposable income 236.3 180.5 245.2 288.5Total expenditure (excl. housing) 157.3 95.8 165.4 244.4

Energy share 7.2 15.9 5.5 1.8Non-durables (excl. energy) share 49.6 51.9 50.7 45.2Services share 31.9 27.0 32.2 36.2Durables share 11.3 5.2 11.6 16.8

Housing 32.0 26.3 32.5 38.2

Household characteristicsAge 51 62 50 45Education (share with post-comp.) 33.5 17.8 35.3 45.7Housing tenure

Social renters 20.9 34.2 15.9 17.7Mortgagors 42.6 20.6 47.5 55.0Outright owners 36.6 45.3 36.6 27.3

Notes: The table shows descriptive statistics on weekly per capita income and expen-diture (in 2015 pounds), the breakdown of expenditure into energy, non-durables excl.energy, services and durables as well as a selection of household characteristics, bothover all households and by energy share group. For variables in levels such as income,expenditure and age the median is shown while the shares are computed based on themean of the corresponding variable. Note that the expenditure shares are expressed as ashare of total expenditure excl. housing and thus services do not include housing either,and semi-durables are subsumed under the non-durable category. Age corresponds tothe age of the household reference person and education is proxied by whether a mem-ber of a household has completed a post-compulsory education.

Figure B.21 shows the corresponding expenditure and income responses. Wecan see that the magnitude of the expenditure response is clearly increasing inthe energy share: while the expenditure of households with a high energy sharefalls significantly and persistently, households with a low energy share barelyalter their expenditure. However, there is also again significant heterogeneity inthe income responses, with the high energy share households experiencing thestrongest fall in their income. An explanation for this finding is that high energyshare households also tend to be poorer and thus have more cyclical income forreasons dicussed in the paper. This makes it difficult to disentangle the directeffects that operate through the energy share from indirect effects. Importantly,the magnitudes of the expenditure responses are again much larger than what

32

can be accounted for by the discretionary income effect alone.

Figure B.21: Household expenditure and income responses by energy share

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income for households with a high energy share (top 25 percent), atypical energy share (middle 50 percent) and low energy share (bottom 25 percent). Theenergy share is measured as expenditure on fuel, light and power, as a share of total ex-penditure excluding housing and the responses are computed based on the median ofthe respective group.

B.3.7. Direct versus indirect effects

To better understand the indirect effects, we have thus looked at the income re-sponses by sector of employment using data from the LFS. In particular, I havegrouped sectors by their energy intensity and their demand sensitivity based oninformation on SIC 2003 sections. A detailed description of all the four groupscan be found in Table B.5.

As explained in the main text, I have excluded utilities from the group ofenergy-intensive sectors when looking at the income response, as the utility sec-

33

Table B.5: Sectors by energy intensity and demand sensitivity

Group Sectors SIC sections

High energy intensity Agriculture, forestry, and fishing; mining andquarrying; manufacturing; electricity, gas andwater supply (utilities); transport, storage andcommunications

A-E, I

Lower energy intensity Construction; Wholesale and retail trade; Hotelsand restaurants; Financial intermediation; Realestate, renting and business; Public administra-tion and defense; Education; Health and socialwork; Other community, social and personal ser-vices

F-H, J-Q

High demand sensitivity Construction; Wholesale and retail trade; Hotelsand restaurants; Other community, social andpersonal services

F-H, O-Q

Lower demand sensitivity Agriculture, forestry, and fishing; mining andquarrying; manufacturing; electricity, gas andwater supply (utilities); transport, storage andcommunications; Financial intermediation; Realestate, renting and business; Public administra-tion and defense; Education; Health and socialwork

A-E, J-N

Notes: The sectors are grouped based on SIC 2003 sections. Note that the grouping is notperfect, as the LFS only has information on groups of sections over the entire sample ofinterest. The data on the energy intensity by sector from 1999-2018 is from the ONS.

tor may respond very differently from other energy-intensive sectors. Indeed,as shown in Figure B.22, the households working in utilities do not experience asignificant change in their income, consistent the results from Section 5.4. Thisfurther supports the notion that the utility sector can, at least in the short run,profit from a more restrictive carbon pricing regime. In contrast, incomes in otherhigh-energy intensive sectors display a significant fall. However, the responseturns out to be more muted compared to demand-sensitive sectors. This maycome as a surprise against the backdrop that these sectors are more exposed be-cause of their higher cost share of energy. However, note that these sectors alsotend to be less sensitive to changes demand, as they also produce more of es-sential goods and services. This illustrates again that the shock predominantlytransmits through demand and not cost channels.

34

Figure B.22: Income response in energy-intensive sectors

Notes: Impulse responses of median income in utilities and other energy-intensive sec-tors.

To better understand the role of the energy share across income groups, Ilook at the responses of low- and higher-income households conditioning on themost exposed high-energy share households and households with a lower energyshare, as discussed in the paper. Note that these groups vary in size, as we con-dition on households in a particular income group that also display a particularenergy share. The results are shown in Figure B.23.

35

Panel A: Expenditure responses

Panel B: Income responses

Figure B.23: Responses by income and energy share groups

Notes: Impulse responses of total expenditure excluding housing and current total dis-posable household income by income group (bottom 25 percent versus other 75 percent),conditioning on households with a high (top 25 percent) or lower energy share (bottom75 percent).

36

To investigate into alternative direct channels, I look at the responses of thenon-durable, services and durable goods expenditure, first in the aggregate andthen by income group. From Figure B.24, we can see that all components fall in re-sponse to a carbon policy shock. However, while the fall in services and durableexpenditure is more temporary, the response of non-durable expenditure turnsout to be very persistent. There is also substantial heterogeneity by income group,in particular for non-durable goods and services. While low-income householdsexperience a significant and persistent fall, the responses of higher income house-holds are much less pronounced and non-durable goods expenditure even tendsto increase at shorter horizons. For durables, low-income households also showthe strongest response, however, overall the responses tend to be a bit more ho-mogeneous across income groups. Also note that the magnitude of the durableresponse is larger, in line with the fact that durable expenditure tends to be morevolatile.

The results on durable expenditure support the notion that there may be otherdirect channels at play such as the postponement of durable goods purchases be-cause of increased uncertainty or a shift in expenditure on durables that are com-plementary in use with energy – channels that tend to be more pronounced forhigh-income households given their higher share of durables in total expendi-ture. These channels may help explain the short-lived fall in total expenditure ofhigh-income households, which is absent from non-durable expenditure. How-ever, given the relatively short-lived response, these channels cannot account forthe persistent effects observed for total expenditure.

37

Figure B.24: Responses of non-durable, services, and durable expenditure

Notes: Impulse responses of the non-durable, services and durable components of to-tal expenditure (excluding housing). Non-durable expenditure includes fuel, light andpower, food, alcoholic drinks, tobacco, clothing and footwear, and the non-durable partsof household goods, personal goods and services, motoring expenditure, leisure goodsand miscellaneous expenditure. Services expenditure includes household services, faresand other travel, leisure services, as well as the services part of personal goods and ser-vices and miscellaneous expenditure. Durable expenditure includes the durable part ofhousehold goods, personal goods and services, motoring expenditure and leisure goods.

38

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B.3.8. External validity

To mitigate concerns regarding external validity, I confirm the main results on theheterogeneity in household expenditure by income group using data for Den-mark and Spain. As can be seen from Figure B.26, the expenditure responseturns out to be significant and persistent for low-income households, while high-income households are much less affected. These findings confirm the results forthe UK, supporting the external validity of the results.

Figure B.26: Expenditure by income groups for other European countries

Notes: Impulse responses of total expenditure for low-income, middle-income and high-income households in Denmark and Spain. The Danish data are from the Danish house-hold budget survey (HBS) available for 1999-2018, accessed via the StatBank Denmarkdatabase, and expenditure is grouped by total annual income (under 250K DKK, 250-999K DKK, 1000K DKK or over). The Spanish data are from the Spanish HBS availablefor 2006-2018, accessed via the INE website, and expenditure is grouped by regular netmonthly household income (under 1000 euros, 1000-2499 euros, 2500 euros or over).

40

B.3.9. Attitudes towards climate policy

As discussed in the paper, public opposition can be an impediment for climatepolicy. Thus, it is interesting to see how carbon pricing affects the public attitudetowards climate policy. To analyze this question, I use data from the British socialattitudes (BSA) survey. The BSA is an annual survey that asks about the attitudesof the British population towards a wide selection of topics, ranging from wel-fare to genomic science. The BSA is used to inform the development of publicpolicy and is an important barometer of public attitudes. Some of the questionsin the BSA are repeated over time and thus, it is possible to analyze how certainattitudes have changed over time.

To proxy the public attitude towards climate policy, I rely on a question fromthe transportation module of the survey, which asks about the attitude towardsfuel taxes. In particular, the question asks whether the respondent agrees withthe following statement: “For the sake of the environment, car users should payhigher taxes”. The BSA also includes information about the income of the re-spondent, thus it is possible to analyze how the attitudes of different incomegroups have evolved. Figure B.27 shows how the attitude towards fuel taxes haschanged among low- and higher-income households. We can see that the supportof climate policy has remained relatively stable at moderate levels for a large partof the sample. In the early to middle 2010s, the support started increasing forhigher-income households. In contrast, the support of low-income householdshas remained stable until the end of the sample.

Figure B.27: Public support for climate policy by income group

Notes: The figure shows the evolution of the attitude towards climate policy by incomegroup, as proxied by the share of households in the British social attitudes survey thatagree to the following statement: “For the sake of the environment, car users should payhigher taxes”.

41

Figure B.28 shows how the attitude towards fuel taxes among income groupschanges after a restrictive carbon policy shock. We can see that carbon pricingleads to a fall in the approval rate of environmentally-motivated tax policies. Theeffect is very significant and persistent for low-income households, which are alsothe households that are most hardly affected by carbon pricing in economic terms.In contrast, the response of the high-income group is less precisely estimated andeven turns positive in the longer run.

Figure B.28: Effect on attitude towards climate policy by income group

Notes: Impulse responses of public attitude towards climate policy for low- and higher-income groups. The public attitude towards climate policy is proxied by the share ofhouseholds in the British social attitudes survey that agree to the following statement:“For the sake of the environment, car users should pay higher taxes”. Low-income corre-spond to the bottom 25 percent and higher-income to the other 75 percent of the incomedistribution.

B.4. Robustness

In this Appendix, I present the Figures and Tables corresponding to the robust-ness analyses described in Section 7 of the paper.

B.4.1. Selection of events

The first check concerns the selection of the relevant events used for identifica-tion. As the baseline, I have included all identified events that concern the sup-ply of emission allowances. Figures B.29-B.32 present the results under varyingassumptions and show that the results turn out to be very robust to the selectionof events. Figure B.33 also shows that the identification strategy does not dependon very large events, even though these events turn out to be important for theprecision of the estimates.

42

Figure B.29: Excluding events regarding cap

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

43

Figure B.30: Excluding events regarding international credits

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

44

Figure B.31: Only using events on free allocation and auctioning

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

45

Figure B.32: Excluding potentially confounded events

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

46

Figure B.33: Excluding extreme events (price change in excess of 30 percent)

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

B.4.2. Confounding news

An important robustness check concerns the treatment of background noise, i.e.other news occuring on the event day that potentially confound the carbon policysurprise series. Under the external and internal instrument approaches, I assumethat this background noise is not large enough to confound my results.

This assumption is supported by the observation that the variance of the sur-prise series is much larger on event days than on a sample of controls days, whichare comparable to event days along many dimensions but do not include a car-bon policy event (Table B.6 lists the event and control days used in the analysis.For the controls days, I use days that are on the same weekday and in the same

47

week in months prior a given regulatory event.).

Table B.6: Policy and control events

Month Policy Control Month Policy Control

2005M05 25/05/2005 2012M03 29/03/20122005M06 20/06/2005 2012M04 04/04/2012

25/04/20122005M07 27/07/2005 2012M05 02/05/2012

23/05/20122005M08 24/08/2005 2012M06 05/06/20122005M09 21/09/2005 2012M07 06/07/2012

13/07/201225/07/2012

2005M10 26/10/2005 2012M08 13/08/201215/08/201217/08/201231/08/2012

2005M11 23/11/2005 2012M09 10/09/201212/09/201214/09/201228/09/2012

2005M12 22/12/2005 2012M10 08/10/201210/10/201212/10/201226/10/2012

2006M01 25/01/2006 2012M11 12/11/201214/11/201216/11/201230/11/2012

2006M02 22/02/2006 2012M12 28/12/20122006M03 20/03/2006 2013M01 25/01/20132006M04 24/04/2006 2013M02 28/02/20132006M05 22/05/2006 2013M03 25/03/20132006M06 26/06/2006 2013M04 16/04/20132006M07 24/07/2006 2013M05 08/05/20132006M08 21/08/2006 2013M06 05/06/20132006M09 25/09/2006 2013M07 03/07/2013

10/07/201330/07/2013

2006M10 23/10/2006 2013M08 08/08/201329/08/2013

2006M11 13/11/200629/11/2006

2013M09 05/09/201326/09/2013

2006M12 14/12/2006 2013M10 11/10/20132007M01 16/01/2007 2013M11 08/11/2013

21/11/20132007M02 05/02/2007

26/02/20072013M12 10/12/2013

11/12/201318/12/2013

2007M03 26/03/2007 2014M01 08/01/201422/01/2014

2007M04 02/04/200716/04/200730/04/2007

2014M02 26/02/201427/02/2014

2007M05 04/05/200715/05/2007

2014M03 13/03/201428/03/2014

48

Month Policy Control Month Policy Control

2007M06 06/06/2007 2014M04 04/04/201411/04/201423/04/2014

2007M07 11/07/2007 2014M05 02/05/201405/05/2014

2007M08 08/08/2007 2014M06 04/06/20142007M09 05/09/2007 2014M07 04/07/2014

09/07/20142007M10 10/10/2007 2014M08 25/08/20142007M11 07/11/2007 2014M09 29/09/20142007M12 11/12/2007 2014M10 27/10/20142008M01 08/01/2008 2014M11 04/11/20142008M02 05/02/2008 2014M12 01/12/20142008M03 11/03/2008 2015M01 05/01/20152008M04 08/04/2008 2015M02 02/02/20152008M05 22/05/2008 2015M03 02/03/20152008M06 26/06/2008 2015M04 06/04/20152008M07 24/07/2008 2015M05 04/05/20152008M08 21/08/2008 2015M06 17/06/2015

25/06/20152008M09 25/09/2008 2015M07 15/07/2015

23/07/20152008M10 23/10/2008 2015M08 05/08/20152008M11 20/11/2008 2015M09 02/09/20152008M12 25/12/2008 2015M10 07/10/20152009M01 22/01/2009 2015M11 04/11/20152009M02 19/02/2009 2015M12 18/12/20152009M03 26/03/2009 2016M01 15/01/20162009M04 23/04/2009 2016M02 25/02/20162009M05 20/05/2009 2016M03 31/03/20162009M06 24/06/2009 2016M04 28/04/20162009M07 22/07/2009 2016M05 02/05/20162009M08 26/08/2009 2016M06 23/06/20162009M09 23/09/2009 2016M07 15/07/20162009M10 22/10/2009 2016M08 11/08/20162009M11 26/11/2009 2016M09 08/09/20162009M12 24/12/2009 2016M10 07/10/20162010M01 18/01/2010 2016M11 04/11/20162010M02 15/02/2010 2016M12 19/12/2016

27/12/20162010M03 22/03/2010 2017M01 16/01/2017

24/01/20172010M04 19/04/2010 2017M02 15/02/20172010M05 14/05/2010

19/05/20102017M03 30/03/2017

2010M06 11/06/201016/06/2010

2017M04 27/04/2017

2010M07 09/07/201014/07/2010

2017M05 02/05/201712/05/2017

2010M08 20/08/2010 2017M06 19/06/201728/06/2017

2010M09 24/09/2010 2017M07 17/07/201726/07/2017

2010M10 22/10/2010 2017M08 07/08/20172010M11 12/11/2010

25/11/20102017M09 04/09/2017

49

Month Policy Control Month Policy Control

2010M12 15/12/2010 2017M10 09/10/20172011M01 21/01/2011 2017M11 06/11/20172011M02 15/02/2011

22/02/201128/02/2011

2017M12 18/12/2017

2011M03 15/03/201122/03/201129/03/2011

2018M01 15/01/2018

2011M04 27/04/201129/04/2011

2018M02 02/02/201806/02/201813/02/2018

2011M05 10/05/2011 2018M03 02/03/201806/03/201813/03/2018

2011M06 07/06/2011 2018M04 06/04/201810/04/201817/04/2018

2011M07 13/07/2011 2018M05 04/05/201808/05/201815/05/2018

2011M08 29/08/2011 2018M06 18/06/20182011M09 26/09/2011 2018M07 16/07/20182011M10 17/10/2011

26/10/201128/10/2011

2018M08 28/08/2018

2011M11 14/11/201123/11/201125/11/2011

2018M09 25/09/2018

2011M12 05/12/2011 2018M10 30/10/20182012M01 26/01/2012 2018M11 06/11/20182012M02 23/02/2012 2018M12 05/12/2018

Figure B.34: The carbon policy and the control series

Notes: This figure shows the carbon policy surprise series together with the sur-prise series constructed on a selection of control days that do not contain a regu-latory announcement but are otherwise similar.

Figure B.34 displays the carbon policy surprise series together with the controlseries over the sample of interest. We can see that the carbon policy surprise

50

series is significantly more volatile than the control series and a Brown-Forsythetest for the equality of group variances confirms that this difference is statisticallysignificant.

Figure B.35: Heteroskedasticity-based identification

Notes: Impulse responses to a carbon policy shock identified using theheteroskedasticity-based approach, normalized to increase the HICP energy by 1percent on impact. The solid line is the point estimate and the dark and light shadedareas are 68 and 90 percent confidence bands, respectively.

It is exactly this shift in variance that can be exploited for identification using aheteroskedasticity-based approach in the spirit of Rigobon (2003), assuming thatthe shift is driven by the carbon policy shock. Figure B.35 shows the results fromthis alternative approach. The responses turn out to be very similar, both in termsof shape and magnitudes, but turn out to be less precisely estimated. These re-sults suggest that the bias induced by background noise is likely negligible in

51

the present application. However, part of the statistical strength under the exter-nal/internal instrument approach appears to come from the stronger identifyingassumptions.

B.4.3. Futures contracts

Figure B.36: Using different futures contracts for the instrument

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. Depicted are the point estimates using different futurescontracts to construct the instrument.

EUA futures are traded at different maturities. I focus on the quarterly contracts,with expiry date in March, June, September and December. As a baseline, I usethe front contract, which is the contract with the closest expiry date and is usuallythe most liquid. Figure B.36 presents the results based on contracts with longer

52

maturities. The responses based on the second to the fourth contract are all verysimilar. The largest difference emerge compared to the front contract, however,most responses are qualitatively very similar. However, it should be noted thatusing contracts further out weakens the first stage considerably. Overall, theseresults support the focus on the front contract, to mitigate concerns about riskpremia.

53

B.4.4. Sample and specification choices

Finally, I perform a number of sensitivity checks concerning the sample andmodel specification. Figure B.37 shows the results based on the shorter samplerunning from 2005, when the ETS was established, to 2018. The results turn outto be very similar to the baseline case.

Figure B.37: Results using 2005-2018 sample

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

Figure B.38 excludes events in phase one (2005-2007) in the construction of theinstruments. While the point estimates are similar, the responses are much lessprecisely estimated, illustrating how the identification strategy leverages the factthat establishing the carbon market was a learning-by-doing process where the

54

rules have been continuously updated.

Figure B.38: Excluding phase one events

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

55

The baseline model includes 8 variables and 6 lags, which is relatively large fora comparably short sample. Therefore, Figures B.39-B.43 analyze the robustnesswith respect to the variables included and number of lags used. Alternatively,I estimate the model using shrinkage priors.3 The results turn out to be robustalong all these dimensions.

Figure B.39: Responses from smaller VAR

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

3In particular, I use a Minnesota prior with a tightness of 0.1 and a decay of 1.

56

Figure B.40: VAR including linear trend

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

57

Figure B.41: VAR with 3 lags

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

58

Figure B.42: VAR with 9 lags

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the point estimate and the dark and lightshaded areas are 68 and 90 percent confidence bands, respectively.

59

Figure B.43: Bayesian VAR with shrinkage priors

Notes: Impulse responses to a carbon policy shock, normalized to increase the HICPenergy by 1 percent on impact. The solid line is the posterior median and the dark andlight shaded areas are 68 and 90 percent HPD bands, respectively.

60

C. Heteroskedasticity-based identification

As discussed in Section 7, we can also identify the structural impact vector underweaker assumptions, allowing for the presence of other shocks contaminating theinstrument over the daily event window. Suppose that movements in the EUAfutures zt we observe in the data are governed by both carbon policy and othershocks:

zt = ε1,t + ∑j 6=1

ε j,t + vt,

where ε j,t are other shocks affecting carbon futures and vt ∼ iidN(0, σ2v ) captures

measurement error such as microstructure noise. Because zt is also affected byother shocks, it is no longer a valid external instrument. However, we can stillidentify the structural impact vector by exploiting the heteroskedasticity in thedata.

The identifying assumption is that the variance of carbon policy shocks in-creases at the time of regulatory update events while the variance of all othershocks is unchanged. Define R1 as a sample of regulatory events in the EU ETSand R2 as a sample of trading days that do not contain an regulatory event butare comparable on other dimensions. R1 can be thought of as the treatment andR2 as the control sample (see Appendix B.4 for more information and some de-scriptive statistics of the instrument in the treatment and the control sample). Theidentifying assumptions can then be written as follows

σ2ε1,R1 > σ2

ε1,R2

σ2ε j,R1 = σ2

ε j,R2, for j = 2, . . . , n. (3)

σ2v,R1 = σ2

v,R2.

Under these assumptions, the structural impact vector is given by

s1 =ER1[ztut]−ER2[ztut]

ER1[z2t ]−ER2[z2

t ]. (4)

As shown by Rigobon and Sack (2004), we can also obtain this estimator throughan IV approach, using z = (z′R1, −z′R2)

′ as an instrument in a regression of thereduced-form innovations on z = (z′R1, z′R2)

′.

61

D. A climate DSGE model with heterogeneous agents

and sticky prices

D.1. Overview and results

In this appendix, I develop the theoretical model. The aim is to derive a frame-work that can account for the empirical findings – both at the aggregate level andalong the cross section – and can be used for policy experiments. The model be-longs to the dynamic stochastic general equilibrium (DSGE) class and augmentsthe climate-economy structure by Golosov et al. (2014) with nominal rigidities.The model consists of four building blocks: households, firms, a government anda climate block. The firm block is further divided into consumption good and en-ergy producers. Importantly, there is heterogeneity in the household block withrespect to households’ energy shares, income incidence and marginal propensi-ties to consume. A detailed derivation of the model can be found in AppendixD.2.

D.1.1. Households

The household sector consists of a continuum of infinitely lived households, in-dexed by i ∈ [0, 1]. Households are assumed to have identical preferences withfelicity function U(x, h), deriving utility from consumption x and disutility fromlabor h. To retain tractability, I consider a model with limited heterogeneity. Thereare two types of households: a share λ of households are hand-to-mouth H wholive paycheck by paycheck and consume all of their income and a share 1 − λ

savers S who choose their consumption intertemporally. Apart from the differ-ence in their marginal propensities to consume (MPC), households differ alongtwo key dimensions: (i) the expenditure energy share and (ii) the income inci-dence. In line with the data, we assume that hand-to-mouth households have ahigher energy share than savers and that their income is more elastic to changesin aggregate income than savers’.

Labor supply decisions are relegated to a labor union, which sets wages ac-cording to the following schedule:

wt = ϕhθt

(λ

1pH,t

Ux(xH,t, ht) + (1− λ)1

pS,tUx(xS,t, ht)

)−1

, (5)

where wt is the real wage charged by the union, pH,t and pS,t are the relativeprices of the hand-to-mouth and the savers’ consumption baskets, respectively,

62

and Ux(·) is the marginal utility of consumption. The labor market structureequalizes labor income across households; thus all income heterogeneity in themodel will come from heterogeneity in financial income.4

Savers. Savers maximize their lifetime utility

Et

[∞

∑s=0

βsU(xS,t+s, ht+s)

],

choosing how much to consume xS,t, save bS,t+1 and invest iS,t. Their consump-tion bundle xS,t is a composite of a non-energy good cS,t and energy eS,t:

xS,t =

(a

1εxS,cc

εx−1εx

S,t + a1

εxS,ee

εx−1εx

S,t

) εxεx−1

,

where aS,c and aS,e are distribution parameters satisfying aS,c + aS,e = 1, and εx isthe elasticity of substitution between non-energy and energy goods.

The demand functions for the consumption and energy good the are

cS,t = aS,c

(1

pS,t

)−εx

xS,t (6)

eS,t = aS,e

(pe,t

pS,t

)−εx

xS,t, (7)

respectively. Note that the consumption good is chosen to be the numeraire, i.e.

it’s price is one in real terms. The corresponding price index is pS,t =(

aS,c + aS,e p1−εxe,t

) 11−εx .

Each period, savers face the following flow budget constraint

pS,txS,t + iS,t + bS,t+1 = yS,t. (8)

The savers’ income is given by yS,t = wtht +Rb

t−1Πt

bS,t + (1− τk)rtkS,t +(1−τd)dt

1−λ +

ωS,t, where pS,t is the price of the savers’ final consumption bundle,Rb

t−1Πt

is therisk-free rate deflated by inflation, rt is the rental rate of capital, dt are dividends,and ωS,t are transfers from the government.

Capital accumulation is given by

kS,t+1 = iS,t + (1− δ)kS,t. (9)

4This is a reduced-form way of capturing the income responses observed in the data. In themodel, this labor market structure helps to mitigate varying labor supply responses offsetting in-come heterogeneity. Furthermore, it allows to introduce sticky wages relatively straightforwardly.

63

Savers’ optimizing behavior is characterized by the following equations

λt = βEt[(1 + (1− τk)rt+1 − δ)λt+1] (10)

λt = βEt

[Rb

tΠt+1

λt+1

], (11)

where λt = Ux(xS,t, ht)/pS,t is the shadow value of wealth.

Hand-to-mouth. Hand-to-mouth households have no assets and thus consumeall of their income in every period:

pH,txH,t = yH,t. (12)

The income of the hand-to-mouth is given by yH,t = wthdt + ωH,t, where ωH,t are

government transfers. The demand functions for non-energy goods and energyare

cH,t = aH,c

(1

pS,t

)−εx

xH,t (13)

eH,t = aH,e

(pe,t

pS,t

)−εx

xH,t, (14)

with the associated price pH,t =(

aH,c + aH,e p1−εxe,t

) 11−εx .

D.1.2. Firms

The firm block of the model consists of two sectors: energy and non-energy pro-ducers. Importantly, non-energy firms also use energy as an intermediate inputto produce the non-energy good. Further, we assume that non-energy firms facesome costs in adjusting their prices while the energy sector does not face anyprice rigidity while energy producers do not, in line with the empirical evidence(Dhyne et al., 2006; Alvarez et al., 2006).

To simplify matters, we split the non-energy goods sectors into two subsec-tors: a representative competitive final goods firm which aggregates intermedi-ate goods according to a CES technology and a continuum of intermediate goodsproducers that produce different varieties using labor as an input. To the extentto which the intermediate goods are imperfect substitutes, there is a downward-sloping demand for each intermediate variety, giving the intermediate producerssome pricing power. However, importantly, intermediate goods producers can-

64

not freely adjust prices. Nominal price rigidities are modeled according to Calvo(1983) mechanism. In each period, a firm faces a constant probability 1− θp ofbeing able to reoptimize the nominal wage.

Non-energy firms. The final non-energy good is produced by a perfectly com-petitive firm, combining a continuum of intermediate inputs yt(i) according to

the following standard CES production function: yd,t =

(∫ 10 yt(i)

εp−1εp di

) εpεp−1

,

with εp > 1. Taking prices as given, the final good producer chooses interme-diate good quantities yt(i) to maximize profits, resulting in the usual demand

schedule yt(i) =(

Pt(i)Pt

)−εyd,t. From the zero-profit condition, we obtain the ag-

gregate price level Pt =(∫ 1

0 Pt(i)1−εp dj) 1

1−εp .Intermediate inputs are produced by a continuum of monopolistic firms in-

dexed by i ∈ [0, 1] according to the following constant returns to scale technology,using capital kt(i), energy ey,t(i), and labor hy,t(i) as inputs

yt(i) = e−γst atkt(i)αey,t(i)νhy,t(i)1−α−ν, (15)

where at is TFP, and st is the atmospheric carbon concentration. Note that thereis a feedback loop between climate and the economy. Higher economic activityincreases carbon emissions via higher energy use, which in turn increases the car-bon concentration (or equivalently the total stock of emissions). A higher carbonconcentration will have economic damages in turn (e.g. via weather events etc.),which reduce output. We model this by a damage function term in the firms’ pro-duction function. The damage function is given by an exponential function (as inGolosov et al., 2014). The parameter γ can be used to scale the damage function.

Intermediate goods producers maximize profits, taking the demand of theirvariety into account. Importantly, intermediate goods producers cannot freelyadjust prices. As in Calvo (1983), in each period they face a constant probabilityof 1− θp of being able to reoptimize their price.

The cost-minimization problem gives rise to the standard factor demands

rt = αmctyt

kt

pe,t = νmctyt

ey,t(16)

wt = (1− α− ν)mctyt

hy,t,

which are common across firms. Here, mct are real marginal costs.

65

When setting prices, intermediate goods producers take into account that thechoice today might affect not only current but also future profits. The optimalitycondition is given by

Et

∞

∑k=0

(βθp)kλt+kyd,t+kPεp−1

t+k

(Pt(i)−Mp Pt+kmct+k

)= 0, (17)

where Mp =εp

εp−1 is the steady-state markup and λt is the shadow value ofwealth for a saver. In log-linear terms, this gives rise to the standard Phillipscurve πt = κmct + βEtπt+1, where κ =

(1−θp)(1−θpβ)θp

is the slope of the curve.

Finally, monopoly profits are given by dt =∫ 1

0 [Pt(i)

Ptyt(i)−mctyt(i)]di.

Energy producers. As in Golosov et al. (2014), the energy firm produces energyusing labor according to the following technology

et = ae,the,t. (18)

We assume that there is only a single source of energy (e.g. coal) that is availablein (approx.) infinite supply. Note that we measure energy in terms of carboncontent (carbon amount emitted). Energy firms are subject to a carbon tax. Forconvenience we model it as a sales tax τt, however, we can equally model it as aunit tax (see also the discussion in Golosov et al., 2014).

Optimizing behavior is characterized by the following equation

wt = (1− τt)pe,tet

he,t. (19)

D.1.3. Climate block

Following Golosov et al. (2014), I model the current level of atmospheric carbonconcentration as a function of current and past emissions:

st =∞

∑s=0

(1− ds)et−s,

where 1− ds = (1− ϕL)ϕ0(1− ϕ)s. Here, 1− ϕ0 is the share of remaining emis-sions exiting the atmosphere immediately while ϕ0 is the remaining share ofemissions that decay over time at a geometric rate 1− ϕ. We can write this inrecursive form as

st = (1− ϕ)st−1 + ϕ0et. (20)

66

D.1.4. Fiscal and monetary policy

The government runs a balanced budget in every period, i.e. all transfers arefinanced by tax revenues. We consider the following transfer policy

λωH,t = τddt + τkrKt kt + µτt pe,tet (21)

(1− λ)ωS,t = (1− µ)τt pe,tet (22)

The distribution of carbon tax revenues are governed by parameter µ. As thebaseline, we assume that all carbon revenues are obtained by the savers, i.e. µ =

0. Later, we will experiment with alternative transfer policies.5

Carbon taxes τt are set according to the following rule:

τt = (1− ρτ)τ + ρττt−1 + ετ,t. (23)

Finally, we assume that there is a monetary authority that conducts monetarypolicy according to the following simple Taylor rule

Rbt

Rb =

(Πt

Π

)φπ

eεmp,t . (24)

D.1.5. Aggregation and market clearing

Because capital is only held by S, we have that (1−λ)kS,t = kt and (1−λ)iS,t = it.Because bonds are in zero net supply, we have bt = (1− λ)bS,t = 0.

Aggregate total, non-energy, and energy consumption are given by xt = λxH,t +

(1− λ)xS,t, ct = λcH,t + (1− λ)cS,t, and ec,t = λeH,t + (1− λ)eS,t, respectively.Labor market clearing requires ht = hy,t + he,t. The energy market clears ifet = ec,t + ey,t.

Aggregate production is given by

yt =∫ 1

0yt(i)di = e−γst atkα

t eνy,th

1−α−νy,t = ∆tyd,t, (25)

where ∆t =∫ 1

0

(Pt(i)

Pt

)−εpdi is a price dispersion term, generating a wedge be-

tween aggregate output and aggregate demand.Finally, goods market clearing requires that

ct + it = yd,t. (26)

5Furthermore, we assume that τd = τk = 0. However, the tax scheme can be used to equalizeincomes if τd = τk = µ = λ.

67

D.1.6. Calibration and functional forms

The felicity function is assumed to be

U(xi,t, ht) =x1−σ

i,t − 1

1− σ− ψ

h1+θt

1 + θ,

for i ∈ H, S. This function belongs to the commonly used constant elasticityclass, where 1/σ is the intertemporal elasticity of substitution and 1/θ is the laborsupply elasticity.

We calibrate the model as follows. The time period is a quarter. The discountfactor β takes the standard value 0.99, which implies an annualized steady-stateinterest rate of 4 percent. The intertemporal elasticity of substitution 1/σ is set to2.6 I set the share of hand-to-mouth λ to 25 percent, corresponding to the low-income threshold used in the LCFS. Such a share is also in line with the estimatesof hand-to-mouth households in Kaplan, Weidner, and Violante (2014). The dis-tribution parameters aH,e and aS,e are calibrated to match the energy expenditureshares of 9.5 percent for the hand-to-mouth and 6.5 percent for the savers as ob-served in the LCFS. The elasticity of substitution between energy and non-energygoods εx is set to a relatively low value of 0.3. This corresponds approximately tothe impact elasticity estimated in the LCFS and is in line with the insignificant en-ergy share response. The labor supply elasticity 1/θ is set to 4. While this value isat the upper range of the values commonly used in the literature, a relatively highlabor supply elasticity helps to generate income responses that are consistent inmagnitude with the responses observed in the data. The labor weight in the util-ity function, ϕ is calibrated such that steady-state hours worked h are normalizedto one.

Turning to the production side, I set the depreciation rate δ to 0.025, imply-ing an annual depreciation on capital of 10 percent. I set α to 0.275, which im-plies a standard steady-state capital share (rk/y) of 70 percent (see e.g. Smets andWouters, 2003). Using data on non-household energy consumption and energyprices in the EU, I estimate a energy share (peey/y) of around 7 percent. Thisis slightly higher than the energy share in the US, as estimated for instance byHassler, Krusell, and Olovsson (2012), and implies a value of ν = 0.085. The elas-ticity of substitution between non-energy varieties is assumed to be 6, which is astandard value and implies a steady-state markup of 20 percent, consistent withthe evidence in Christopoulou and Vermeulen (2012). The Calvo parameter θp is

6This is value is at the upper range of the values commonly used in the literature, however,the results are robust to using the more standard unitary elasticity.

68

set to 0.825, which implies an average price duration of 5-6 quarters, in line withthe empirical estimates in Alvarez et al. (2006). These parameter choices imply arelatively flat Phillips curve with a slope of 0.04.

For the climate block, I rely on the values in Golosov et al. (2014). I abstractfrom uncertainty about the damage parameter and use the deterministic, long-run value from Golosov et al. (2014). Note, however, that carbon emissions in mymodel are in arbitrary units. Thus, following Heutel (2012) I scale the damage pa-rameter to make the increase in output damages from doubling the steady-statecarbon stock consistent with the projected increase in damages from doublingCO2 levels in 2005. Turning to the carbon cycle, note that the excess carbon has ahalf-life of about 300 years (Archer, 2005). This implies a value of 1− ϕ = 0.9994.7

Furthermore, according to the 2007 IPCC reports, about half of the CO2 pulseto the atmosphere is removed after a time scale of 30 years. This implies thatϕ0 = 0.5

(1−ϕ)120 = 0.5359.Turning to fiscal and monetary policy, I compute the steady-state carbon tax as

the implied tax rate implied by the average EUA price which is around 3.2 percent(the average real EUA price as a share of gross electricity prices in emission units).The persistence of the tax shock is set to 0.85, which implies that the shock isclose to being fully reabsorbed after about 20 quarters, which is consistent withthe shock dynamics observed in the external instruments VAR. Finally, the Taylorrule coefficient on inflation is set to 1.05. This value is motivated by the absentreaction of monetary policy to carbon policy shocks observed in the data, andalso confirms well with the anecdotal evidence in Konradt and di Mauro (2021).8

All other taxes are assumed to be zero in the baseline case, later we will usethem to equalize the income incidence. Furthermore, we assume that all carbontax revenues accrue to the savers, µ = 0, motivated by the fact that there is noredistribution scheme in the current EU ETS in place. The calibration is summa-rized in Table D.1.

7From the carbon cycle, we have Etst+h = (1− ϕ)hst = 0.5st. Thus, we impose (1− ϕ)1200 =0.5 to get ϕ.

8A lower Taylor rule coefficient also ensures the model to have a determinate solution. Condi-tional on the other parameter values used, a Taylor rule coefficient above 1.1 will cause the modelto be indeterminate.

69

Table D.1: Calibration

Parameter Description Value Target/Source

β Discount factor 0.99 Smets and Wouters (2003)1/σ Intertemporal elasticity of substi-

tution2 Gruber (2013)

λ Share of hand-to-mouth 0.25 Share of low-income households,LCFS

aH,e Distribution parameter H 0.103 Energy share of 9.5%, LCFSaS,e Distribution parameter S 0.071 Energy share of 6.5%, LCFSεx Elasticity of substitution

energy/non-energy0.3 Empirical estimate, LCFS

1/θ Labor supply elasticity 4 Empirical income responses,LCFS

ϕ Labor utility weight 0.799 Steady-state hours normalized to1

δ Depreciation rate 0.025 Smets and Wouters (2003)α Capital returns-to-scale 0.275 Steady-state capital share of 30%;

Smets and Wouters (2003)ν Energy returns-to-scale 0.085 Steady-state energy share of 7%;

Eurostatεp Price elasticity 6 Steady-state markup of 20%;

Christopoulou and Vermeulen(2012)

θp Calvo parameter 0.825 Average price duration of 5-6quarters; Alvarez et al. (2006)

γ Climate damage parameter 5.3 ∗ 10−5 Golosov et al. (2014)ϕ0 Emissions staying in atmosphere 0.5359 Golosov et al. (2014)

1− ϕ Emissions decay parameter 0.9994 Golosov et al. (2014)φπ Taylor rule coefficient 1.05 VAR evidence/determinacyτ Steady-state carbon tax 0.039 Implied tax rate from average

EUA priceρτ Persistence carbon tax shock 0.85 Mean-reversion of approx. 20

quarters

D.1.7. Main results

We will now study how a carbon policy shock affects the economy. As in theempirics, I will normalize the shock such that it increases the energy price pe,t byone percent on impact. As mentioned above, I assume that all carbon revenuesgo to the savers as the baseline. Alternatively, I will consider the case in which allrevenues are redistributed to the hand-to-mouth.

70

Figure D.1: Baseline responses

Figure D.1 displays the consumption and income responses, both in the ag-gregate and by household group. We can see that a carbon policy shock leadsto a significant fall in consumption and income and the magnitudes of the peakresponses are in the same ballpark as in the empirical evidence.9 Importantly, wecan see that the hand-to-mouth play a crucial role in the transmission of carbonpolicy. They experience a much stronger income response, which in combina-tion with the higher energy share leads to a pronounced fall in their expenditure,with a peak response of around -1 percent. In contrast, the savers’ response ismuch more muted. Finally, the shock also leads to a significant fall in energyuse/emissions.

Redistributing carbon tax revenues alters the transmission of the shock sub-

9The model is, however, by construction not able to match the hump shape of the responses. Tothis end, additional model features would be needed such as habit persistence, adjustment costsor rational inattention. To retain tractability, I have deliberately abstracted from these features.

71

stantially. Both aggregate consumption and income fall by substantially less. Theincome response of hand-to-mouth turns positive and allows the hand-to-mouthto increase their expenditure. The saver’s income and expenditure responses areslightly more pronounced but the positive response of hand-to-mouth outweighsthese effects such that aggregate consumption response drops from -0.3 to -0.2 onimpact. Importantly, the response of emissions changes by much less, supportingthe interpretation that the effects of carbon pricing can be mitigated by targetedfiscal policies without compromising emission reductions.10

As illustrated in Figure D.2, the heterogeneity is crucial in getting the em-pirical magnitudes of the consumption responses. Without the heterogeneity inMPCs, energy shares and income incidence, it is not possible to get the sizeableresponses observed in the data without implausibly high firm and household en-ergy shares.

Figure D.2: Heterogeneous versus representative agent

Finally, Figure D.3 illustrates the importance of the direct effects via energy

10Note that it is theoretically possible for the negative effects on the savers, which decreaseinvestment and thus the capital stock and future consumption, to outweigh the positive effecton the hand-to-mouth. In this case, redistributing the tax revenues to the hand-to-mouth wouldmake the aggregate consumption response more pronounced. However, in the parameter regionthat can deliver empirically plausible income and expenditure responses, redistribution turns outto be robustly beneficial.

72

shares and the indirect effects through the income incidence. We can see that theheterogeneity in energy share can only account for a limited part of the aggregateconsumption response, as the model with unequal incidence is already very closeto the baseline with heterogeneous energy shares and income incidence.

Figure D.3: Decomposition of direct and indirect effects

73

D.2. Model derivations

D.2.1. Labor market structure

We assume that there is a continuum of differentiated labor inputs indexed byj ∈ [0, 1].

Labor packer. There is a labor packer that bundles differentiated labor inputsinto aggregate labor demand according to a CES technology:

maxht(j)

wthd,t −∫ 1

0wt(j)ht(j)dj s.t. hd,t =

(∫ 1

0ht(j)

εw−1εw dj

) εwεw−1

The labor demand is

ht(j) =(

wt(j)wt

)−εw

hd,t.

and the aggregate wage wt is

wt =

(∫ 1

0wt(j)1−εw dj

) 11−εw

.

Unions. As in Schmitt-Grohé and Uribe (2005), each household supplies eachpossible type of labor. Wage-setting decisions are made by labor-type specificunions j ∈ [0, 1].11 Given the wage wt(j) fixed by union j, households standready to supply as many hours to the labor market j, ht(j), as demanded by firms

ht(j) =(

wt(j)wt

)−εw

hd,t,

where εw > 1 is the elasticity of substitution between labor inputs. Here, wt isan index of the real wages prevailing in the economy at time t and hd,t is theaggregate labor demand.

Households are distributed uniformly across unions and hence aggregate de-mand for labor type j is spread uniformly across households. It follows that the

11This is different from the standard way of introducing sticky wages (see Christopher J. Erceg,Dale W Henderson and Andrew T. Levin, 2000), which assumes that each household supplies adifferentiated type of labor input. This assumption introduces equilibrium heterogeneity acrosshouseholds in the number of hours worked. To avoid this heterogeneity from spilling over intoconsumption heterogeneity, it is typically assumed that preferences are separable in consumptionand labor and that financial markets exists that allow agents to fully insure against unemploymentrisk. With the Schmitt-Grohé and Uribe formulation, one does not have to make these restrictiveassumptions.

74

individual quantity of hours worked, ht(i), is common across households andwe denote it as ht. This must satisfy the time resource constraint ht =

∫ 10 ht(j)dj.

Plugging in for the labor demand from above, we get

ht = hd,t

∫ 1

0

(wt(j)

wt

)−εw

dj.

The labor market structure rules out differences in labor income between house-holds without the need to resort to contingent markets for hours. The commonlabor income is given by

wthd,t =∫ 1

0wt(j)ht(j)dj = hd,t

∫ 1

0wt(j)

(wt(j)

wt

)−εw

dj.

Wage setting. Unions set their charged wages wj by maximizing a social welfarefunction, given by the weighted average of hand-to-mouth and savers’ utility,with the weights are equal to the shares of the households.12 The union problemreads

maxwt(j)

(λ(xH,t)

1−σ − 11− σ

+ (1− λ)(xS,t)

1−σ − 11− σ

)− ϕ

h1+θt

1 + θ

s.t. ht = hd,t

∫ 1

0

(wt(j)

wt

)−εw

dj.

pS,txS,t + iS,t + bS,t+1 = hd,t

∫ 1

0wt(j)

(wt(j)

wt

)−εw

dj +Rb

t−1

ΠtbS,t + (1− τk)rtkS,t +

(1− τd)dt

1− λ+ ωS,t

pH,txH,t = hd,t

∫ 1

0wt(j)

(wt(j)

wt

)−εw

dj + ωH,t

The FOC is given by

λx−σH,t

1pH,t

hd,twεwt (1− εw)wt(j)−εw + (1− λ)x−σ

S,t1

pS,thd,tw

εwt (1− εw)wt(j)−εw =

ϕhθt hd,tw

εwt (−εw)wt(j)−εw−1

This rewrites

wt(j) =εw

εw − 1ϕhθ

t

(λ

1pH,t

x−σH,t + (1− λ)

1pS,t

x−σS,t

)−1

,

12This welfare function follows from the assumption that each household i supplies each pos-sible type of labor input j and there are a share of λ hand-to-mouth and a share of 1− λ savers.

75

where εwεw−1 =Mw is the constant wage markup. By putting an optimal subsidy

in place, we can neutralize the markup and arrive at

wt(j) = ϕhθt

(λ

1pH,t

x−σH,t + (1− λ)

1pS,t

x−σS,t

)−1

.

Note that because everything on the right-hand-side is independent of j, itfollows that all unions charge the same wage wt(j) = wt. From the definition ofaggregate labor supply, we further have hd,t = ht.

Thus, wage setting is characterized by the following equation:

wt = ϕhθt

(λ

1pH,t

x−σH,t + (1− λ)

1pS,t

x−σS,t

)−1

.

Using this in the households’ budget constraints:

pS,txS,t + iS,t + bS,t+1 = wtht +Rb

t−1Πt

bS,t + (1− τk)rtkS,t +(1− τd)dt

1− λ+ ωS,t

pH,txH,t = wtht + ωH,t.

D.2.2. Households

Savers. Savers maximize their lifetime utility subject to their budget constraint,taking prices and wages as given, choosing how much to consume xS,t, to in-vest in capital iS,t, and how much to save in risk-free bonds bS,t+1 (in real terms,BS,t+1/Pt). Their program reads

maxxS,t,iS,t,bS,t+1

Et

[∞

∑s=0

βs

(x1−σ

S,t+s − 1

1− σ− ψ

h1+θt+s

1 + θ

)]

s.t. pS,txS,t + iS,t + bS,t+1 = wthd,t +Rb

t−1Πt

bS,t + (1− τk)rtkS,t +(1− τd)dt

1− λ+ ωS,t

kS,t+1 = iS,t + (1− δ)kS,t,

where we have expressed everything in real terms: pS,t is the price of the savers’

final consumption bundle, wt is the real wage, wthd,t is real labor income,Rb

t−1Πt

isthe risk-free rate deflated by inflation, rt is the rental rate of capital, dt are div-idends, and ωS,t are lump-sum transfers from the government. σ is the relativerisk aversion (1/σ is the intertemporal elasticity of substitution) and ψ is a pa-rameter governing the disutility of labor.

76

The first-order conditions read

pS,tλt = x−σS,t

λt = βEt[(1 + (1− τk)rt+1 − δ)λt+1]

λt = βEt

[Rb

tΠt+1

λt+1

]

The final consumption bundle xS,t is a CES aggregate of consumption andenergy goods

xS,t =

(a

1εxS,cc

εx−1εx

S,t + a1

εxS,ee

εx−1εx

S,t

) εxεx−1

,

where aS,c and aS,e are distribution parameters with aS,c + aS,e = 113 , and εx is theelasticity of substitution between non-energy and energy goods: ∂(ct/ec,t)/(ct/ec,t)

∂(pe,t/1)/(pe,t/1) .14

Making the distribution parameters household-specific allows for heterogeneityin the households’ energy share.

The demands for the consumption and energy good the are given by

cS,t = aS,c

(1

pS,t

)−εx

xS,t

eS,t = aS,e

(pe,t

pS,t

)−εx

xS,t,

respectively. Note that the consumption good is chosen to be the numeraire, i.e.it’s price is one in real terms.

13Note that the distribution parameters aS,c and aS,e, sometimes also referred to as shares, arein fact not shares but depend on underlying dimensions unless εx = 1. In other words, theseparameters are not deep parameters but depend on a mixture of parameters that depends on thechoice of units. To circumvent this issue, we follow the re-parameterization approach proposedby Cantore and Levine (2012). In particular, we calibrate the steady-state energy share and to backout the implied distribution parameters. We have:

aS,e =peeSpSxS

(pe

pS

)εx−1= ωS,e

(pe

pS

)εx−1,

where ωS,e is the energy expenditure share. From this, we then have aS,c = 1− aS,e. Note that thisshare is dimensionless. Thus, we can calibrate or estimate it. By using this strategy, we can alsoperform comparative statics, varying the elasticity εx.

14If εx approaches ∞, the goods are perfect substitutes; if εx approaches 0, the goods are perfectcomplements; and if εx approaches 1, the goods are one-for-one substitutable, which correspondsto the Cobb-Douglas case.

77

The corresponding price index is

pS,t =(

aS,c + aS,e p1−εxe,t

) 11−εx .

Hand-to-mouth. Hand-to-mouth households have no assets and thus consumetheir labor income as well as the transfer they get from the government. Theirproblem is thus static and reads

maxxH,t

x1−σH,t − 11− σ

− ψh1+θ

t1 + θ

s.t. pH,txH,t ≤ wthd,t + ωH,t

Because of monotonicity, hand-to-mouth households will consume as muchas their budget constraint allows

pH,txH,t = wthdt + ωH,t.

Similarly, consumption and energy demands are

cH,t = aH,c

(1

pS,t

)−εx

xH,t

eH,t = aH,e

(pe,t

pS,t

)−εx

xH,t

and the price of their bundle is

pH,t =(

aH,c + aH,e p1−εxe,t

) 11−εx .15

D.2.3. Firms

The firm block of the model consists of two sectors: energy and non-energy pro-ducers. Importantly, non-energy firms also use energy as an intermediate inputto produce the non-energy good. Further, we assume that non-energy firms facesome costs in adjusting their prices while the energy sector does not face anyprice rigidity.

15Finally, their distribution parameters are given by aH,e = ωH,e

(pepH

)εx−1and vaH,c = 1− aH,e.

78

Non-energy firms. To simplify matters, we split the non-energy goods sectorsinto two subsectors: a representative competitive final goods firm which aggre-gates intermediate goods according to a CES technology and a continuum of in-termediate goods producers that produce different varieties using labor as aninput. To the extent to which the intermediate goods are imperfect substitutes,there is a downward-sloping demand for each intermediate variety, giving the in-termediate producers some pricing power. However, importantly, intermediategoods producers cannot freely adjust prices. Nominal price rigidities are mod-eled according to Calvo (1983) mechanism. In each period, a firm faces a constantprobability 1− θp of being able to reoptimize the nominal wage.

Final goods producer. Final goods firms maximize profits subject to the produc-tion function by taking prices as given. Since final goods firms are all identical,we can focus on one representative firm. These firms bundle the differentiatedgoods into a final good using a CES technology. The program of such a represen-tative final goods firm (set up in nominal terms) reads

maxyt(i)

Ptyd,t −∫ 1

0Pt(i)yt(i)di s.t. yd,t =

(∫ 1

0yt(i)

ε−1ε di

) εε−1

,

where yd,t is aggregate demand and ε is the elasticity of substitution. When goodsare perfectly substitutable ε → ∞, we approach the perfect competition bench-mark.

From the first order condition, we get the factor demand

yt(i) =(

Pt(i)Pt

)−ε

yd,t.

From the zero profit condition one can deduce the aggregate price level Pt =(∫ 1

0 Pt(i)1−εdj) 1

1−ε .

Intermediate goods producers. We asume that non-energy intermediate goodsproducers have the following production technology

yt(i) = e−γst atkt(i)αey,t(i)νhy,t(i)1−α−ν,

where at is TFP, and st is the atmospheric carbon concentration.As intermediate goods producers are monopolists, they maximize profits by

taking the demand function of final goods firms into account. We consider nowthe problem of an intermediate goods firm i. For the sake of simplicity the pro-

79

gram is split into two sub-problems: the cost minimization and the price settingproblem. To find the real cost function, factor costs are minimized subject to theproduction function. The program of firm i reads

minnt(i)

rtkt(i) + wthy,t(i) + pe,tey,t(i) s.t. yt(i) ≤ e−γst atkt(i)αey,t(i)νhy,t(i)1−α−ν

The FOCs read

rt = αλt(i)yt(i)kt(i)

pe,t = νλt(i)yt(i)ey,t(i)

wt = (1− α− ν)λt(i)yt(i)

hy,t(i)

where λt(i) is the corresponding Lagrange multiplier. This multiplier will againhave the interpretation as real marginal cost – how much will costs change if youare forced to produce an extra unit of output, i.e. mct(i) = λt(i). To prove this,let us solve for the Lagrange multiplier as a function of output. We have

λt(i) =1α

rtkt(i)yt(i)

=1ν

pe,tey,t(i)yt(i)

=1

1− α− νwt

hy,t(i)yt(i)

.

Thus,

kt(i) =α

1− α− ν

wt

rthy,t(i)

ey,t(i) =ν

1− α− ν

wt

pe,thy,t(i)

Plugging this in the constraint

yt(i) = e−γst at

(α

1− α− ν

wt

rt

)α ( ν

1− α− ν

wt

pe,t

)ν

hy,t(i).

From this we get the factor demand for labor, capital and energy

hy,t(i) = eγst

(α

1− α− ν

wt

rt

)−α ( ν

1− α− ν

wt

pe,t

)−ν yt(i)at

kt(i) = eγst

(α

1− α− ν

wt

rt

)1−α ( ν

1− α− ν

wt

pe,t

)−ν yt(i)at

ey,t(i) = eγst

(α

1− α− ν

wt

rt

)−α ( ν

1− α− ν

wt

pe,t

)1−ν yt(i)at

,

80

which in turn can be used to get the Lagrange multiplier

λt(i) = eγst α−αν−ν(1− α− ν)−(1−α−ν)rαt pν

e,tw1−α−νt

1at

.

Using the factor demands, we can solve for the cost function:

C(rt, pe,t, wt, yt(i)) = eγst α−αν−ν(1− α− ν)−(1−α−ν)rαt pν

e,tw1−α−νt

yt(i)at

Thus, one can see that the multiplier is equal to the marginal cost function:λt(i) = Cy(rt, pe,t, wt, yt(i)) = mct(i). Note that in the definition of the marginalcost (Lagrange multiplier) above, there is nothing that depends on i. Thus, itfollows that marginal costs are the same across firms, i.e mct(i) = mct.

Another important result can be obtained by dividing the two factor demands:

kt(i)hy,t(i)

=α

1− α− ν

wt

rt

kt(i)ey,t(i)

=α

ν

pe,t

rt

From this one can see that all firms hire capital and energy in the same ratio, i.e.kt(i)

hy,t(i)= kt

hy,tand ey,t(i)

hy,t(i)=

ey,thy,t

. This also implies that the output-capital, output-labor, and output-energy ratios are the same across firms.

Now that we have found the real cost function, we can move to the intermedi-ate goods firms’ price setting problem. Intermediate goods producers set pricesto maximize the expected discounted stream of (real) profits (that is real revenueminus real labor input). However, as outlined above, firms are not able to freelyadjust price each period. In particular, each period there is a fixed probability of1− θp that a firm can adjust its price. This means that the probability a firm willbe stuck with a price one period is θp, for two periods is θ2

p, and so on (thus weassume independence from time since last price adjustment). Consider the pric-ing problem of a firm given the opportunity to adjust its price in a given period.Since there is a chance that the firm will get stuck with its price for multiple peri-ods, the pricing problem becomes dynamic. Firms will discount profits s periods

into the future by Mt,t+sθsp, where Mt,t+s = βs λS

t+sλS

tis the stochastic discount factor,

which follows from the fact that the firm is owned by the savers. The price settingproblem reads

maxPt(i)

Et

∞

∑k=0

(βθp)k λt+k

λt

(Pt(i)Pt+k

yt+k(i)−mct+kyt+k(i))

81

s.t.

yt+k(i) =

(Pt(i)Pt+k

)−εp

yd,t+k

∞

k=0

.

The FOC reads

Et

∞

∑k=0

(βθp)k λt+k

λt

((1− εp)Pt(i)−εp Pεp−1

t+k yd,t+k + εp mct+kPt(i)−εp−1Pεpt+kyd,t+k

)= 0.

Simplifying gives

Et

∞

∑k=0

(βθp)kλt+k

((1− εp)Pεp−1

t+k yd,t+k + εp mct+kPt(i)−1Pεpt+kyd,t+k

)= 0.

By rearranging, we obtain

Pt(i) =εp

εp − 1Et ∑∞

k=0(βθp)kλt+kmct+kPεpt+kyd,t+k

Et ∑∞k=0(βθp)kλt+kPεp−1

t+k yd,t+k

Note that nothing on the RHS depends on i. Thus, all firms will choose the samereset price P∗t = Pt(i).

We can write the optimal price more compactly as

P∗t =εp

εp − 1X1,t

X2,t

with

X1,t = Et

∞

∑k=0

(βθp)kλt+kmct+kPεp

t+kyd,t+k

X2,t = Et

∞

∑k=0

(βθp)kλt+kPεp−1

t+k yd,t+k.

16If θp = 0, then this would reduce to

P∗t =εp

εp − 1︸ ︷︷ ︸M

Pt mct,

i.e. the optimal price would be a fixed markup over nominal marginal cost. The distortion comingfrom this fixed markup over marginal cost can be easily eliminated using a constant subsidy. Inthis case we have thatM = 1 and

Pt = MCt

in the limiting case when prices are flexible. However, with sticky prices this markup will be timevarying, which introduces another distortion. In steady state, however, there will be no markup,i.e. real marginal costs will be one.

82

We can also write the X’s recursively

X1,t = λtmctPεpt yd,t + βθpEtX1,t+1

X2,t = λtPεp−1t yd,t + βθpEtX2,t+1.16

Let us now rewrite these expressions in terms of inflation (as the price levelmay be non-stationary). Define x1,t =

X1,t

Pεpt

and x2,t =X2,t

Pεp−1t

. Thus, we have

x1,t = λtmctyd,t + βθpEtx1,t+1Πεpt+1

x2,t = λtyd,t + βθpEtx2,t+1Πεp−1t+1 .

The reset price equation then writes

P∗t =εp

εp − 1Pt

x1,t

x2,t

⇒ Π∗t =εp

εp − 1Πt

x1,t

x2,t,

where we define reset price inflation as Π∗t =P∗t

Pt−1.

Exploiting the Calvo assumption, we can write the aggregate price index as

Π1−εpt = (1− θp)(Π∗t )

1−εp + θp.

By way of summary, optimal behavior of firm i is characterized by

rt = αmctyt

kt

pe,t = νmctyt

ey,t

wt = (1− α− ν)mctyt

hy,t

Π∗t =εp

εp − 1Πt

x1,t

x2,t

x1,t = λtmctyd,t + βθpEtx1,t+1Πεpt+1

x2,t = λtyd,t + βθpEtx2,t+1Πεp−1t+1

Π1−εpt = (1− θp)(Π∗t )

1−εp + θp

yt(i) = e−γst atkt(i)αey,t(i)νhy,t(i)1−α−ν

83

The aggregate production is given by

yt =∫ 1

0yt(i)di =

∫ 1

0e−γst atkt(i)αey,t(i)νhy,t(i)1−α−νdi

⇒ yt = e−γst atkαt eν

y,th1−α−νy,t = ∆tyd,t,

where we have exploited the fact that factors are hired in the same proportionand plugged in for the demand function. Note that there is a wedge betweenaggregate output and aggregate demand. The intuition is that with Calvo pric-ing, firms charging prices in different periods will generally have different prices,which implies that the model features price dispersion. When firms have differ-ent relative prices, there are distortions that create a wedge between betweenaggregate output measured in terms of production factor inputs and aggregatedemand measured in terms of the composite good. The higher the price disper-sion, the more labor and capital are needed to produce a given level of output.

We can also rewrite the dispersion term in terms of inflation making use of theCalvo assumption. We have

∆t = (1− θp)(Π∗t )−εp Π

εpt + θpΠ

εpt ∆t−1.

Firms profits are

dt =∫ 1

0

Pt(i)Pt

yt(i)di−mct

∫ 1

0yt(i)di.

Plugging in the demand function gives

dt = yd,tPεp−1t

∫ 1

0Pt(i)1−εp di−mctyd,t

∫ 1

0

(Pt(i)

Pt

)−εp

di.

Now since P1−εpt =

∫ 10 Pt(i)1−εp di, this reduces to

dt = yd,t −mctyd,t

∫ 1

0

(Pt(i)

Pt

)−εp

di

Thus, we can write profits as

dt = (1−mct∆t)yd,t.

Further, note that

mctyt = rtkt + pe,tey,t + wthy,t.

84

Thus, we can also write profits as

dt = yd,t − rtkt − pe,tey,t − wthy,t.

Energy producers. The energy firm produces energy using labor only accordingto the following production function:

et = ae,the,t.

We assume that there is only a single source of energy (e.g. coal) that is availablein (approx.) infinite supply. Note that we measure energy in terms of carboncontent (carbon amount emitted). Energy firms are subject to a carbon tax. Foreach unit of emitted CO2, they have to pay τt.

Their maximization problem reads

maxhe,t

(1− τt)pe,tet − wthe,t

s.t. et = ae,the,t

The FOC gives the optimal energy supply:

(1− τt)pe,tae,t = wt

(1− τt)pe,tet = wthe,twt

(1− τt)pe,t=

et

he,t.

D.2.4. Market clearing

To derive goods market clearing, we multiply the households budget constraintsby their shares and sum over them:

λpH,txH,t + (1− λ)(pS,txS,t + iS,t + bS,t+1) = λ(wtht + ωH,t) + (1− λ)

(wtht +

Rbt−1

ΠtbS,t + (1− τk)rtkS,t +

(1− τd)dt

1− λ+ ωS,t

)

ct + it + pe,tec,t = wtht + rtkt + τt pe,tet + dt

ct + it + pe,tec,t = wtht + rtkt + τt pe,tet + yd,t − rtkt − wthy,t − pe,tey,t

ct + it = wthy,t + wthe,t + τt pe,tet + yd,t − wthy,t − pe,tet

ct + it = (1− τt)pe,tet + τt pe,tet + yd,t − pe,tet

ct + it = yd,t

85

D.2.5. Equilibrium

A general equilibrium of this economy is defined as a sequence of quantitiesQ = xt, xS,t, xH,t, ct, cS,t, cH,t, ec,t, eS,t, eH,t, it, kt+1, yt, yd,t, ht, hy,t, he,t, ey,t, mct, et, st, τt,ωH,t, dt, ∆t, x1,t, x2,t∞

t=0, a sequence of pricesP = λt, wt, rt, pe,t, pS,t, pH,t, Rbt , Πt, Π∗t ∞

t=0,and a sequence of forcing variables F = at, ae,t, ετ,t, εmp,t∞

t=0 such that

1. Given a sequence of prices P , and a forcing sequence F , the sequence ofquantities Q solves the households’ and the firms’ problems.

2. Given a sequence of quantitiesQ and a sequence of forcing variables F , thesequence of prices P clears all markets.

The equilibrium is characterized by the following set of equations:

86

Table D.2: Summary of equilibrium conditions

1: Wage setting wt = ϕhθt

(λ 1

pH,tx−σ

H,t + (1− λ) 1pS,t

x−σS,t

)−1

2: Non-energy demand, S cS,t = aS,c

(1

pS,t

)−εxxS,t

3: Energy demand, S eS,t = aS,e

(pe,tpS,t

)−εxxS,t

4: Shadow value of wealth pS,tλt = x−σS,t

5: Investment Euler equation, S λt = βEt[(1 + (1− τk)rt+1 − δ)λt+1]

6: Bonds Euler equation, S λt = βEt

[Rb

tΠt+1

λt+1

]

7: Capital accumulation kt+1 = it + (1− δ)kt

8: Final good price index, S pS,t =(

aS,c + aS,e p1−εxe,t

) 11−εx

9: Non-energy demand, H cH,t = aH,c

(1

pH,t

)−εxxH,t

10: Energy demand, H eH,t = aH,e

(pe,tpH,t

)−εxxH,t

11: Consumption, H pH,txH,t = wtht + ωH,t

12: Final good price index, H pH,t =(

aH,c + aH,e p1−εxe,t

) 11−εx

13: Capital demand non-energy firm rt = αmctytkt

14: Labor demand non-energy firm wt = (1− α− ν)mctyt

hy,t

15: Energy demand non-energy firm pe,t = νmctytey,t

16: Reset price Π∗t =εp

εp−1 Πtx1,tx2,t

17-18: Auxiliary terms x1,t = λtmctyd,t + βθpEtx1,t+1Πεpt+1

x2,t = λtyd,t + βθpEtx2,t+1Πεp−1t+1

19: Aggregate inflation Π1−εpt = (1− θp)(Π∗t )

1−εp + θp

20: Price dispersion ∆t = (1− θp)(Π∗t )−εp Π

εpt + θpΠ

εpt ∆t−1

21: Aggregate demand non-energy yd,t∆t = yt22: Production function non-energy firm yt = e−γst atkα

t eνy,th

1−α−νy,t

23: Energy supply (1− τt)pe,tet = wthe,t24: Production function energy firm et = ae,the,t25: Carbon emissions st = (1− ϕ)st−1 + ϕ0et26: Aggregate total consumption xt = λxH,t + (1− λ)xS,t27: Aggregate non-energy consumption ct = λcH,t + (1− λ)cS,t28. Aggregate energy consumption ec,t = λeH,t + (1− λ)eS,t29: Labor market clearing ht = hy,t + he,t30: Energy market clearing et = ec,t + ey,t31: Goods market clearing ct + it = yd,t32: Tax schedule τt = (1− ρτ)τ + ρττt−1 + ετ,t33: Transfers, H λωH,t = τddt + τkrK

t kt + µτt pe,tet34: Dividends dt = (1−mct∆t)yd,t

35: Taylor rule Rbt

Rb =(

ΠtΠ

)φπ

eεmp,t

87

D.2.6. Steady state and model solution

We assume that a = ae = 1 in steady state. Furthermore, we normalize ψ suchthat h = 1. Furthermore, τ is calibrated. Finally, we assume that there is zeroinflation in steady state, i.e. Π = 1. From the definition of aggregate inflation andthe price dispersion, this implies Π∗ = 1, ∆ = 1 and yd = y.

From the investment Euler equation, we have

r =1β − 1 + δ

1− τk .

From the bonds Euler, we get

Rb =1β

.

From the reset price, we get

mc =εp − 1

εp.

To solve for the steady state, we guess k and e. From (13) with the aboveequation we get y.17 From (24), we get he. From (29), we get hy. From (25), we gets. From (22), we get ey. From (28), we get ec. From (15), we get pe. From (14), weget w. From (7), we get i. From (31), we get c. From (8), we get pS:

pS =(

aS,c + aS,e p1−εxe

) 11−εx

=(

1−ωS,e pεx−1e p1−εx

S + ωS,e p1−εxS

) 11−εx

= pS

(pεx−1

S −ωS,e pεx−1e + ωS,e

) 11−εx

⇒ 1 = pεx−1S −ωS,e pεx−1

e + ωS,e

pS =(

1 + ωS,e pεx−1e −ωS,e

) 1εx−1

.

From this we then have aS,e = ωS,e

(pepS

)εx−1and aS,c = 1− aS,e. Similarly we

get from (12) pH and aH,e and aH,c. From (34), we get d. From (33), we get ωH.From (11), we get xH. From (9), we get cH. From (10), we get eH. From (27), weget cS. From (28), we get eS. From (3), we get xS. From (26), we get x. From (4),

17The equation numbers here refer to the equations in Table D.2.

88

we get λ. From (1), we get ψ. From (17)-(18), we get the values of the auxiliaryterms x1 and x2.Then we minimize such that (2) and (23) hold.

To solve the model, we log-linearize the equilibrium equations around thedeterministic steady state and solve for a set of linearized policy functions usingDynare.

89

References Appendix

Alloza, Mario, Pablo Burriel, and Javier J Pérez. 2019. “Fiscal policies in the euro area:

Revisiting the size of spillovers.” Journal of Macroeconomics, 61: 103132.

Alvarez, Luis J, Emmanuel Dhyne, Marco Hoeberichts, Claudia Kwapil, Hervé Le Bi-han, Patrick Lünnemann, Fernando Martins, Roberto Sabbatini, Harald Stahl,Philip Vermeulen, et al. 2006. “Sticky prices in the euro area: a summary of new micro-

evidence.” Journal of the European Economic association, 4(2-3): 575–584.

Alves, Felipe, Greg Kaplan, Benjamin Moll, and Giovanni L. Violante. 2020. “A further

look at the propagation of monetary policy shocks in HANK.” Journal of Money, Creditand Banking, 52(S2): 521–559.

Archer, David. 2005. “Fate of fossil fuel CO2 in geologic time.” Journal of geophysical re-search: Oceans, 110(C9).

Baker, Scott R., Nicholas Bloom, and Steven J. Davis. 2016. “Measuring economic policy

uncertainty.” The Quarterly Journal of Economics, 131(4): 1593–1636.

Barnichon, Regis and Christian Brownlees. 2019. “Impulse response estimation by

smooth local projections.” Review of Economics and Statistics, 101(3): 522–530.

Baumeister, Christiane and James D. Hamilton. 2019. “Structural interpretation of vec-

tor autoregressions with incomplete identification: Revisiting the role of oil supply and

demand shocks.” American Economic Review, 109(5): 1873–1910.

Bloom, Nicholas. 2009. “The impact of uncertainty shocks.” Econometrica, 77(3): 623–685.

Caldara, Dario, Michele Cavallo, and Matteo Iacoviello. 2019. “Oil price elasticities and

oil price fluctuations.” Journal of Monetary Economics, 103: 1–20.

Calvo, Guillermo A. 1983. “Staggered prices in a utility-maximizing framework.” Journalof Monetary Economics, 12(3): 383–398.

Cantore, Cristiano and Paul Levine. 2012. “Getting normalization right: Dealing with

‘dimensional constants’ in macroeconomics.” Journal of Economic Dynamics and Control,36(12): 1931–1949.

Christopoulou, Rebekka and Philip Vermeulen. 2012. “Markups in the Euro area and

the US over the period 1981–2004: a comparison of 50 sectors.” Empirical Economics,

42(1): 53–77.

Cloyne, James, Clodomiro Ferreira, and Paolo Surico. 2020. “Monetary policy when

households have debt: new evidence on the transmission mechanism.” The Review ofEconomic Studies, 87(1): 102–129.

Dhyne, Emmanuel, Luis J Alvarez, Hervé Le Bihan, Giovanni Veronese, Daniel Dias,Johannes Hoffmann, Nicole Jonker, Patrick Lunnemann, Fabio Rumler, and JoukoVilmunen. 2006. “Price changes in the euro area and the United States: Some facts

from individual consumer price data.” Journal of Economic Perspectives, 20(2): 171–192.

Erceg, Christopher J., Dale W Henderson, and Andrew T. Levin. 2000. “Optimal mon-

etary policy with staggered wage and price contracts.” Journal of Monetary Economics,

90

46(2): 281–313.

Golosov, Mikhail, John Hassler, Per Krusell, and Aleh Tsyvinski. 2014. “Optimal taxes

on fossil fuel in general equilibrium.” Econometrica, 82(1): 41–88.

Gruber, Jonathan. 2013. “A tax-based estimate of the elasticity of intertemporal substitu-

tion.” The Quarterly Journal of Finance, 3(01): 1350001.

Hassler, John, Per Krusell, and Conny Olovsson. 2012. “Energy-saving technical

change.” National Bureau of Economic Research.

Heutel, Garth. 2012. “How should environmental policy respond to business cycles?

Optimal policy under persistent productivity shocks.” Review of Economic Dynamics,

15(2): 244–264.

Jarocinski, Marek and Peter Karadi. 2020. “Deconstructing monetary policy sur-

prises—the role of information shocks.” American Economic Journal: Macroeconomics,

12(2): 1–43.

Jordà, Òscar, Moritz Schularick, and Alan M. Taylor. 2015. “Betting the house.” Journalof International Economics, 96: S2–S18.

Kaplan, Greg, Justin Weidner, and Giovanni L. Violante. 2014. “The Wealthy Hand-to-

Mouth.” Brookings Papers on Economic Activity.

Kilian, Lutz. 2008. “Exogenous oil supply shocks: how big are they and how much do

they matter for the US economy?” The Review of Economics and Statistics, 90(2): 216–240.

Kilian, Lutz. 2009. “Not all oil price shocks are alike: disentangling demand and supply

shocks in the crude oil market.” American Economic Review, 99(3): 1053–69.

Konradt, Maximilian and Beatrice Weder di Mauro. 2021. “Carbon Taxation and Infla-

tion: Evidence from the European and Canadian Experience.”

Känzig, Diego R. 2021. “The Macroeconomic Effects of Oil Supply News: Evidence from

OPEC Announcements.” American Economic Review, 111(4): 1092–1125.

Mansanet-Bataller, Maria and Angel Pardo. 2009. “Impacts of regulatory announce-

ments on CO2 prices.” The Journal of Energy Markets, 2(2): 1–33.

Montiel Olea, José Luis and Mikkel Plagborg-Møller. 2020. “Local Projection Inference

is Simpler and More Robust Than You Think.”

Plagborg-Møller, Mikkel and Christian K. Wolf. 2020. “Instrumental variable identifi-

cation of dynamic variance decompositions.” arXiv preprint arXiv:2011.01380.

Ramey, Valerie A. and Sarah Zubairy. 2018. “Government spending multipliers in good

times and in bad: evidence from US historical data.” Journal of Political Economy,

126(2): 850–901.

Rigobon, Roberto. 2003. “Identification through heteroskedasticity.” Review of Economicsand Statistics, 85(4): 777–792.

Rigobon, Roberto and Brian Sack. 2004. “The impact of monetary policy on asset

prices.” Journal of Monetary Economics, 51(8): 1553–1575.

Schmitt-Grohé, Stephanie and Martin Uribe. 2005. “Optimal fiscal and monetary policy

in a medium-scale macroeconomic model.” NBER Macroeconomics Annual, 20: 383–425.

91

Smets, Frank and Raf Wouters. 2003. “An estimated dynamic stochastic general equilib-

rium model of the euro area.” Journal of the European economic association, 1(5): 1123–

1175.

92